A320697 Number of partitions of n with up to ten distinct kinds of 1.

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

Alois P. Heinz, Table of n, a(n) for n = 0..10000

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

Adjacent sequences: A320694 A320695 A320696 * A320698 A320699 A320700

Keyword

nonn

Author

Alois P. Heinz, Oct 19 2018

Status

approved