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A363046
Number of partitions of n whose greatest part is a multiple of 4.
5
1, 0, 0, 0, 1, 1, 2, 3, 6, 7, 11, 14, 21, 26, 36, 45, 62, 76, 100, 124, 162, 199, 255, 314, 399, 488, 612, 748, 932, 1134, 1400, 1699, 2086, 2520, 3072, 3700, 4488, 5384, 6494, 7766, 9326, 11112, 13283, 15778, 18788, 22245, 26386, 31150, 36825, 43345, 51070, 59953
OFFSET
0,7
LINKS
FORMULA
G.f.: Sum_{k>=0} x^(4*k)/Product_{j=1..4*k} (1-x^j).
a(n) ~ A000041(n)/4. - Vaclav Kotesovec, May 21 2023
MAPLE
b:= proc(n, i) option remember; `if`(n=0, 1,
`if`(i<1, 0, b(n, i-1)+b(n-i, min(n-i, i))))
end:
a:= n-> add(b(n-4*i, min(n-4*i, 4*i)), i=0..n/4):
seq(a(n), n=0..60); # Alois P. Heinz, May 14 2023
PROG
(PARI) my(N=60, x='x+O('x^N)); Vec(sum(k=0, N, x^(4*k)/prod(j=1, 4*k, 1-x^j)))
CROSSREFS
Column 4 of A363048.
Sequence in context: A018468 A117115 A308733 * A049196 A284743 A256976
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 14 2023
STATUS
approved