A372349 a(n) = Sum_{j=0..n} p(n - j, j) where p(n, x) = Sum_{k=0..n} k! * abs(Stirling1(n, k)) * x^k.

1, 1, 2, 6, 28, 190, 1730, 20068, 287406, 4971884, 102082882, 2450448780, 67879395878, 2145912460492, 76704301481034, 3075725307199340, 137422311677357710, 6800630226338490492, 370741889753741467970, 22155195508036869880684, 1444764915198178824091590

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Maple

p := n -> local k; add(k!*abs(Stirling1(n, k))*x^k, k = 0..n):
a := n -> local j; add(subs(x=j, p(n - j)), j = 0..n):
seq(a(n), n = 0..20);

Mathematica

p[n_][x_] := Sum[k!*Abs[StirlingS1[n, k]]*If[k == 0, 1, x^k], {k, 0, n}];
a[n_] := Sum[p[n - j][j], {j, 0, n}];
Table[a[n], {n, 0, 20}] (* Jean-François Alcover, May 12 2024 *)

Crossrefs

Cf. A372346, A372347, A372348.

Cf. A225479.

Sequence in context: A084262 A231621 A084870 * A111342 A008964 A356577

Adjacent sequences: A372346 A372347 A372348 * A372350 A372351 A372352

Keyword

nonn

Author

Peter Luschny, Apr 29 2024

Status

approved