A372703 Number of partitions of n into distinct parts such that number of parts is a multiples of 4.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 6, 9, 11, 15, 18, 23, 27, 34, 39, 47, 54, 64, 72, 84, 94, 108, 120, 136, 150, 169, 185, 207, 226, 251, 273, 302, 328, 362, 393, 433, 470, 518, 563, 621, 677, 748, 818, 906, 994, 1104, 1216, 1354, 1497, 1671, 1853, 2073, 2305, 2582, 2877, 3226, 3599

Offset

0,13

Links

Table of n, a(n) for n=0..65.

Formula

G.f.: Sum_{k>=0} x^(2*k*(4*k+1)) / Product_{j=1..4*k} (1-x^j) = Sum_{k>=0} Product_{j=1..4*k} (x^j/(1-x^j)).

Prog

(PARI) my(N=70, x='x+O('x^N)); Vec(sum(k=0, N, prod(j=1, 4*k, x^j/(1-x^j))))

Crossrefs

Cf. A000009, A067661, A370747, A373078.

Cf. A363046.

Sequence in context: A242717 A026810 A001400 * A350897 A008773 A008772

Adjacent sequences: A372700 A372701 A372702 * A372704 A372705 A372706

Keyword

nonn

Author

Seiichi Manyama, May 23 2024

Status

approved