A154107 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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

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