A118301 - OEIS

A118301

Number of partitions of n into distinct parts with largest part congruent to n modulo 2.

1, 1, 1, 1, 2, 2, 2, 3, 4, 5, 6, 7, 9, 11, 13, 16, 19, 23, 27, 32, 38, 44, 52, 61, 71, 83, 96, 111, 128, 148, 170, 195, 224, 256, 293, 334, 380, 432, 491, 557, 630, 713, 805, 908, 1024, 1152, 1295, 1455, 1632, 1829, 2049, 2291, 2560, 2859, 3189, 3554, 3958, 4404

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OFFSET

1,5

COMMENTS

a(2*n) = A026838(2*n), a(2*n-1) = A026837(2*n-1);

a(n) = A000009(n) - A118302(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 = 0..2*N+1} (-1)^(n+1)/Product_{k = 1..n} 1 - x^(2*k-1) ). - Peter Bala, Feb 11 2021

EXAMPLE