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

0,2

Links

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

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

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 *)

Crossrefs

Column k=6 of A246935.

Sequence in context: A344065 A180355 A105281 * A158797 A218060 A283328

Adjacent sequences: A246935 A246936 A246937 * A246939 A246940 A246941

Keyword

nonn

Author

Alois P. Heinz, Sep 08 2014

Status

approved