A246940 Number of partitions of n into 8 sorts of parts.

1, 8, 72, 584, 4744, 38024, 304840, 2439368, 19520264, 156167944, 1249386824, 9995142472, 79961491848, 639692324232, 5117541421512, 40940334536648, 327522698972168, 2620181617189384, 20961453119350856, 167691625158581832, 1341533002724164744

Offset: 0

Author

Alois P. Heinz, Sep 08 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Column k=8 of A246935.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      b(n, i-1) +`if`(i>n, 0, 8*b(n-i, i))))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..25);

Mathematica

(O[x]^20 - 7/QPochhammer[8, x])[[3]] (* Vladimir Reshetnikov, Nov 20 2015 *)

Formula

G.f.: Product_{i>=1} 1/(1-8*x^i).

a(n) ~ c * 8^n, where c = Product_{k>=1} 1/(1-1/8^k) = 1.1635943971944701027405... . - Vaclav Kotesovec, Mar 19 2015

G.f.: Sum_{i>=0} 8^i*x^i/Product_{j=1..i} (1 - x^j). - Ilya Gutkovskiy, Apr 12 2018