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

0,2

Links

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

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

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 *)

Crossrefs

Column k=7 of A246935.

Sequence in context: A270240 A344066 A104896 * A122996 A343364 A092318

Adjacent sequences: A246936 A246937 A246938 * A246940 A246941 A246942

Keyword

nonn

Author

Alois P. Heinz, Sep 08 2014

Status

approved