A246938 Number of partitions of n into 6 sorts of parts.

1, 6, 42, 258, 1590, 9582, 57786, 347010, 2083902, 12505470, 75044202, 450278106, 2701739022, 16210513806, 97263509010, 583581545466, 3501491846046, 21008954050422, 126053739826530, 756322456907130, 4537934834757702, 27227609116759302, 163365655261094322

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=6 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, 6*b(n-i, i))))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..25);

Mathematica

(O[x]^20 - 5/QPochhammer[6, x])[[3]] (* Vladimir Reshetnikov, Nov 20 2015 *)

Formula

G.f.: Product_{i>=1} 1/(1-6*x^i).

a(n) ~ c * 6^n, where c = Product_{k>=1} 1/(1-1/6^k) = 1.2411756627857248707756... . - Vaclav Kotesovec, Mar 19 2015

G.f.: Sum_{i>=0} 6^i*x^i/Product_{j=1..i} (1 - x^j). - Ilya Gutkovskiy, Apr 12 2018