A049378 Row sums of triangle A049353.

1, 1, 6, 46, 436, 4956, 65776, 996976, 16957536, 319259296, 6581662336, 147290942976, 3552885191296, 91827536814976, 2530228890080256, 74003737259670016, 2288810287491774976, 74607500831801289216, 2555587654482227055616, 91746983502042106018816

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..421

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) := x*(2-x)*(2-2*x+x^2)/(4*(1-x)^4) (E.g.f. first column of A049353).

From Seiichi Manyama, Jan 18 2025: (Start)

a(n) = Sum_{k=0..n} |Stirling1(n,k)| * A004213(k).

a(n) = (1/exp(1/4)) * (-1)^n * n! * Sum_{k>=0} binomial(-4*k,n)/(4^k * k!). (End)

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(
      binomial(n-1, j-1)*(j+3)!/4!*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 + 3)!/4!*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=5 of A291709.

Cf. A049353, A049426.

Sequence in context: A111531 A052781 A284109 * A365056 A218497 A261499

Adjacent sequences: A049375 A049376 A049377 * A049379 A049380 A049381

Keyword

nonn

Author

Wolfdieter Lang

Extensions

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

Status

approved