A258464 Number of partitions of n into parts of exactly 9 sorts which are introduced in ascending order.

1, 46, 1202, 23523, 384227, 5542879, 73055550, 899381476, 10501235760, 117575627562, 1272685923724, 13401470756233, 137945728220761, 1393299928219604, 13851195993228228, 135865787060383171, 1317624915100561406, 12654868264707446322, 120534359759023523561

Offset

9,2

Links

Alois P. Heinz, Table of n, a(n) for n = 9..1000

Formula

a(n) ~ c * 9^n, where c = 1/(9!*Product_{n>=1} (1-1/9^n)) = 1/(9!*QPochhammer[1/9, 1/9]) = 0.0000031438016899923866898607402658778352... . - Vaclav Kotesovec, Jun 01 2015

Maple

b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
      b(n, i-1, k) +`if`(i>n, 0, k*b(n-i, i, k))))
    end:
T:= (n, k)-> add(b(n$2, k-i)*(-1)^i/(i!*(k-i)!), i=0..k):
a:= n-> T(n, 9):
seq(a(n), n=9..30);

Mathematica

b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1, 0, b[n, i - 1, k] + If[i > n, 0, k b[n - i, i, k]]]];
T[n_, k_] := Sum[b[n, n, k - i] (-1)^i/(i! (k - i)!), {i, 0, k}];
Table[T[n, 9], {n, 9, 30}] (* Jean-François Alcover, Dec 07 2020, after Alois P. Heinz *)

Crossrefs

Column k=9 of A256130.

Cf. A320551.

Sequence in context: A010998 A004424 A361183 * A320552 A211835 A333066

Adjacent sequences: A258461 A258462 A258463 * A258465 A258466 A258467

Keyword

nonn

Author

Alois P. Heinz, May 30 2015

Status

approved