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A258464 Number of partitions of n into parts of exactly 9 sorts which are introduced in ascending order. 3
1, 46, 1202, 23523, 384227, 5542879, 73055550, 899381476, 10501235760, 117575627562, 1272685923724, 13401470756233, 137945728220761, 1393299928219604, 13851195993228228, 135865787060383171, 1317624915100561406, 12654868264707446322, 120534359759023523561 (list; graph; refs; listen; history; text; internal format)
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);

CROSSREFS

Column k=9 of A256130.

Cf. A320551.

Sequence in context: A162452 A010998 A004424 * A320552 A211835 A333066

Adjacent sequences:  A258461 A258462 A258463 * A258465 A258466 A258467

KEYWORD

nonn

AUTHOR

Alois P. Heinz, May 30 2015

STATUS

approved

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Last modified May 28 17:37 EDT 2020. Contains 334684 sequences. (Running on oeis4.)