A246939 Number of partitions of n into 7 sorts of parts.

1, 7, 56, 399, 2849, 19999, 140441, 983535, 6887986, 48219486, 337559586, 2362943030, 16540767131, 115785555389, 810500055939, 5673501716540, 39714520225149, 278001650902563, 1946011613977669, 13622081363362570, 95354569947550935, 667481990092883448

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=7 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, 7*b(n-i, i))))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..25);

Mathematica

(O[x]^20 - 6/QPochhammer[7, x])[[3]] (* Vladimir Reshetnikov, Nov 20 2015 *)

Formula

G.f.: Product_{i>=1} 1/(1-7*x^i).

a(n) ~ c * 7^n, where c = Product_{k>=1} 1/(1-1/7^k) = 1.1950352398308474540223... . - Vaclav Kotesovec, Mar 19 2015

G.f.: Sum_{i>=0} 7^i*x^i/Product_{j=1..i} (1 - x^j). - Ilya Gutkovskiy, Apr 12 2018