A258463 Number of partitions of n into parts of exactly 8 sorts which are introduced in ascending order.

1, 37, 788, 12705, 172520, 2084836, 23169639, 241881526, 2406802476, 23064505721, 214505275665, 1947297442670, 17332491414616, 151788374231505, 1311496639250495, 11205023121304298, 94832831557086797, 796244028801983324, 6640545376656071546

Offset

8,2

Links

Alois P. Heinz, Table of n, a(n) for n = 8..1000

Formula

a(n) ~ c * 8^n, where c = 1/(8!*Product_{n>=1} (1-1/8^n)) = 1/(8!*QPochhammer[1/8, 1/8]) = 0.0000288589880256565005640019500910465339603... . - 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, 8):
seq(a(n), n=8..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, 8], {n, 8, 30}] (* Jean-François Alcover, Dec 07 2020, after Alois P. Heinz *)

Crossrefs

Column k=8 of A256130.

Cf. A320550.

Sequence in context: A282927 A220684 A225971 * A320551 A211834 A216439

Adjacent sequences: A258460 A258461 A258462 * A258464 A258465 A258466

Keyword

nonn

Author

Alois P. Heinz, May 30 2015

Status

approved