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

Author

Gary W. Adamson, Jan 04 2009

Keywords

• nonn

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)).

Examples

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

Crossrefs

Cf. A000110, A014182.

Programs

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 *)

Formula

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

Extensions

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