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A363213
Number of partitions of n with rank 4 (the rank of a partition is the largest part minus the number of parts).
3
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
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
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 21 2023
STATUS
approved