A258461 Number of partitions of n into parts of exactly 6 sorts which are introduced in ascending order.

1, 22, 289, 2957, 26073, 208516, 1558219, 11087756, 76079368, 507834013, 3318628444, 21330627775, 135325210699, 849659799754, 5290544981423, 32722489513367, 201296535378562, 1232850239039750, 7523511821431264, 45777353199866275, 277862479920868778

Offset

6,2

Links

Alois P. Heinz, Table of n, a(n) for n = 6..1000

Formula

a(n) ~ c * 6^n, where c = 1/(6!*Product_{n>=1} (1-1/6^n)) = 1/(6!*QPochhammer[1/6, 1/6]) = 0.001723855087202395653855120059043... . - Vaclav Kotesovec, Jun 01 2015

Maple

b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
      b(n, i-1, k) +`if`(i>n, 0, k*b(n-i, i, k))))
    end:
T:= (n, k)-> add(b(n$2, k-i)*(-1)^i/(i!*(k-i)!), i=0..k):
a:= n-> T(n, 6):
seq(a(n), n=6..30);

Mathematica

b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1, 0, b[n, i - 1, k] + If[i > n, 0, k b[n - i, i, k]]]];
T[n_, k_] := Sum[b[n, n, k - i](-1)^i/(i!(k - i)!), {i, 0, k}];
Table[T[n, 6], {n, 6, 30}] (* Jean-François Alcover, Dec 07 2020, after Alois P. Heinz *)

Crossrefs

Column k=6 of A256130.

Cf. A320548.

Sequence in context: A004316 A121792 A020922 * A320549 A211832 A211559

Adjacent sequences: A258458 A258459 A258460 * A258462 A258463 A258464

Keyword

nonn

Author

Alois P. Heinz, May 30 2015

Status

approved