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A363047
Number of partitions of n whose greatest part is a multiple of 5.
5
1, 0, 0, 0, 0, 1, 1, 2, 3, 5, 8, 11, 15, 21, 28, 38, 49, 64, 82, 105, 134, 168, 211, 263, 327, 406, 501, 616, 757, 926, 1133, 1378, 1676, 2031, 2460, 2970, 3581, 4306, 5173, 6197, 7419, 8855, 10561, 12565, 14934, 17712, 20982, 24805, 29294, 34529, 40658, 47785, 56104
OFFSET
0,8
LINKS
FORMULA
G.f.: Sum_{k>=0} x^(5*k)/Product_{j=1..5*k} (1-x^j).
a(n) ~ A000041(n)/5. - 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-5*i, min(n-5*i, 5*i)), i=0..n/5):
seq(a(n), n=0..52); # Alois P. Heinz, May 14 2023
PROG
(PARI) my(N=60, x='x+O('x^N)); Vec(sum(k=0, N, x^(5*k)/prod(j=1, 5*k, 1-x^j)))
CROSSREFS
Column 5 of A363048.
Sequence in context: A071424 A008762 A308823 * A101018 A320593 A006336
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 14 2023
STATUS
approved