A258460 Number of partitions of n into parts of exactly 5 sorts which are introduced in ascending order.

1, 16, 157, 1223, 8331, 52078, 307122, 1738441, 9552809, 51357781, 271624053, 1418856775, 7341440755, 37708531955, 192586153199, 979219591861, 4961598056587, 25071026497266, 126410385360189, 636282269208285, 3198360708483673, 16059685003763157

Offset

5,2

Links

Alois P. Heinz, Table of n, a(n) for n = 5..1000

Formula

a(n) ~ c * 5^n, where c = 1/(5!*Product_{n>=1} (1-1/5^n)) = 1/(5!*QPochhammer[1/5, 1/5]) = 1/(5!*A100222) = 0.0109601129644612101609007882... . - 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, 5):
seq(a(n), n=5..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}];
a[n_] := T[n, 5];
Table[a[n], {n, 5, 30}] (* Jean-François Alcover, May 22 2018, translated from Maple *)

Crossrefs

Column k=5 of A256130.

Cf. A320547.

Sequence in context: A173763 A155649 A184598 * A320548 A211831 A036973

Adjacent sequences: A258457 A258458 A258459 * A258461 A258462 A258463

Keyword

nonn

Author

Alois P. Heinz, May 30 2015

Status

approved