A154107 A000110 / A014182: (A154107 convolved with A014182 = Bell numbers).

1, 1, 3, 5, 15, 61, 207, 881, 4491, 21493, 117543, 710021, 4266279, 28107745, 196120515, 1397747525, 10648637151, 84304440685, 688868927151, 5913133211249, 52348170504555, 479326416322933, 4557380168574135, 44560107679838549, 449806788855058407, 4680686977970550721

Offset

0,3

Comments

A000110 / A014182 = (the eigensequence of Pascal's triangle) /

(eigensequence of the inverse of Pascal's triangle).

A014182 = expansion of exp(1-x-exp(-x)).

Links

Table of n, a(n) for n=0..25.

Formula

A000110 / A014182 = (1, 1, 2, 5, 15, 52, 203,...) / (1, 0, -1, 1, 2, -9, 9, 50,...).

Example

A000110 = 52 = (1, 1, 3, 5, 15, 61) convolved with (1, 0, -1, 1, 2, -9)
= (61 - 5 + 3 + 2 - 9)

Mathematica

nmax = 30; Table[a[j]/.SolveAlways[Table[Sum[a[k]*Sum[(-1)^(n-k-m)*StirlingS2[n-k+1, m+1], {m, 0, n-k}], {k, 0, n}]==BellB[n], {n, 0, nmax}], a][[1]], {j, 0, nmax}] (* Vaclav Kotesovec, Jul 26 2021 *)

Crossrefs

Cf. A000110, A014182.

Sequence in context: A177814 A018702 A018719 * A305873 A307999 A018771

Adjacent sequences: A154104 A154105 A154106 * A154108 A154109 A154110

Keyword

nonn

Author

Gary W. Adamson, Jan 04 2009

Extensions

a(12) corrected and more terms added from Vaclav Kotesovec, Jul 26 2021

Status

approved