A049402 Row sums of triangle A049374.

1, 1, 7, 61, 649, 8245, 122215, 2069425, 39328465, 827226505, 19047582055, 475956135205, 12815133759385, 369605936607805, 11361372997850695, 370609338222772825, 12780705695068446625, 464412124831585889425, 17729002673226394402375, 709180766131239680070925

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..415

Wolfdieter Lang, On generalizations of the Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.

Formula

E.g.f.: exp(p(x)) with p(x) := (1-(1-x)^5)/(5*(1-x)^5) (E.g.f. first column of A049374).

From Seiichi Manyama, Jan 18 2025: (Start)

a(n) = Sum_{k=0..n} |Stirling1(n,k)| * A005011(k).

a(n) = (1/exp(1/5)) * (-1)^n * n! * Sum_{k>=0} binomial(-5*k,n)/(5^k * k!). (End)

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(
      binomial(n-1, j-1)*(j+4)!/5!*a(n-j), j=1..n))
    end:
seq(a(n), n=0..25);  # Alois P. Heinz, Aug 01 2017

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, j - 1]*(j + 4)!/5!*a[n - j], {j, 1, n}];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Jun 04 2018, after Alois P. Heinz *)

Crossrefs

Column k=6 of A291709.

Cf. A049374, A049427.

Sequence in context: A111532 A379996 A061634 * A218498 A261687 A001830

Adjacent sequences: A049399 A049400 A049401 * A049403 A049404 A049405

Keyword

easy,nonn

Author

Wolfdieter Lang

Extensions

a(0)=1 prepended by Alois P. Heinz, Aug 01 2017

Status

approved