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A118302
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Number of partitions of n into distinct parts with largest part not congruent to n modulo 2.
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5
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0, 0, 1, 1, 1, 2, 3, 3, 4, 5, 6, 8, 9, 11, 14, 16, 19, 23, 27, 32, 38, 45, 52, 61, 71, 82, 96, 111, 128, 148, 170, 195, 224, 256, 292, 334, 380, 432, 491, 556, 630, 713, 805, 908, 1024, 1152, 1295, 1455, 1632, 1829, 2048, 2291, 2560, 2859, 3189, 3554, 3959, 4404
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OFFSET
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1,6
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COMMENTS
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a(2*n) = A026837(2*n), a(2*n+1) = A026838(2*n+1);
a(n) = A000009(n) - A118301(n),
a(A090864(n)) = A118303(n)/2 = A000009(A090864(n))/2.
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LINKS
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Table of n, a(n) for n=1..58.
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FORMULA
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Conjectural g.f.: A(x) = Limit_{N -> oo} ( Sum_{n = 1..2*N} (-1)^n/Product_{k = 1..n} 1 - x^(2*k-1) ). - Peter Bala, Feb 11 2021
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EXAMPLE
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a(11) = #{10+1,8+3,8+2+1,6+5,6+4+1,6+3+2} = 6;
a(12) = #{11+1,9+3,9+2+1,7+5,7+4+1,7+3+2,5+4+3,5+4+2+1} = 8.
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CROSSREFS
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Cf. A000701, A118301.
Sequence in context: A188937 A029035 A153178 * A355358 A205216 A304885
Adjacent sequences: A118299 A118300 A118301 * A118303 A118304 A118305
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller, Apr 22 2006
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STATUS
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approved
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