A118302 - OEIS

A118302

Number of partitions of n into distinct parts with largest part not congruent to n modulo 2.

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

1,6

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..58.

FORMULA

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

EXAMPLE