A363213 Number of partitions of n with rank 4 (the rank of a partition is the largest part minus the number of parts).

0, 0, 0, 0, 1, 0, 1, 1, 2, 2, 4, 4, 6, 7, 11, 12, 18, 20, 28, 33, 44, 51, 68, 80, 103, 122, 154, 182, 229, 270, 334, 396, 485, 572, 698, 822, 993, 1169, 1404, 1649, 1971, 2310, 2745, 3214, 3803, 4439, 5235, 6099, 7162, 8331, 9750, 11315, 13205, 15294, 17794, 20574, 23872

Offset

1,9

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Formula

G.f.: (1/Product_{k>=1} (1-x^k)) * Sum_{k>=1} (-1)^(k-1) * x^(4*k) * ( x^(k*(3*k-1)/2) - x^(k*(3*k+1)/2) ).

Prog

(PARI) my(N=60, x='x+O('x^N)); concat([0, 0, 0, 0], Vec(1/prod(k=1, N, 1-x^k)*sum(k=1, N, (-1)^(k-1)*x^(4*k)*(x^(k*(3*k-1)/2)-x^(k*(3*k+1)/2)))))

Crossrefs

Column k=4 in the triangle A063995.

Column r=4 of A105806.

Cf. A000041.

Sequence in context: A058686 A339447 A027188 * A089076 A123067 A218897

Adjacent sequences: A363210 A363211 A363212 * A363214 A363215 A363216

Keyword

nonn

Author

Seiichi Manyama, May 21 2023

Status

approved