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A320697
Number of partitions of n with up to ten distinct kinds of 1.
2
1, 10, 46, 131, 267, 439, 654, 956, 1394, 2002, 2817, 3897, 5320, 7179, 9587, 12687, 16652, 21687, 28048, 36051, 46066, 58534, 73998, 93113, 116649, 145513, 180793, 223800, 276077, 339417, 415942, 508179, 619090, 752128, 911336, 1101444, 1327973, 1597358
OFFSET
0,2
LINKS
FORMULA
a(n) ~ Pi * 2^(15/2) * exp(Pi*sqrt(2*n/3)) / (3 * n^(3/2)). - Vaclav Kotesovec, Oct 24 2018
G.f.: (1 + x)^10 * Product_{k>=2} 1 / (1 - x^k). - Ilya Gutkovskiy, Apr 24 2021
MAPLE
b:= proc(n, i) option remember; `if`(n=0 or i=1,
binomial(10, n), `if`(i>n, 0, b(n-i, i))+b(n, i-1))
end:
a:= n-> b(n$2):
seq(a(n), n=0..60);
CROSSREFS
Column k=10 of A292622.
Sequence in context: A281550 A248575 A341404 * A081583 A244246 A288117
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 19 2018
STATUS
approved