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

0,2

Links

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

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

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 *)

Crossrefs

Column k=8 of A246935.

Sequence in context: A344067 A111919 A052379 * A158798 A229249 A242160

Adjacent sequences: A246937 A246938 A246939 * A246941 A246942 A246943

Keyword

nonn

Author

Alois P. Heinz, Sep 08 2014

Status

approved