A318117 Number of compositions of n into exactly n nonnegative parts <= ten.

1, 1, 3, 10, 35, 126, 462, 1716, 6435, 24310, 92378, 352705, 1351934, 5199117, 20050460, 77512860, 300292131, 1165534689, 4531337778, 17642948675, 68785126410, 268497991905, 1049210943531, 4104103226699, 16068342973950, 62963565243876, 246913415221671

Offset: 0

Author

Alois P. Heinz, Aug 17 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1665

Crossrefs

Column k=10 of A305161.

Cf. A088218.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0, 1,
      `if`(i=0, 0, add(b(n-j, i-1), j=0..min(n, 10))))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..30);

Formula

a(n) = [x^n] ((x^11-1)/(x-1))^n.

a(n) <= A088218(n) with equality only for n < 11.

a(n) = Sum_{k=0..floor(n/11)} (-1)^k * binomial(n,k) * binomial(2*n-11*k-1,n-11*k). - Ilya Gutkovskiy, Nov 03 2021