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%I #9 Jul 26 2021 08:28:55
%S 1,1,3,5,15,61,207,881,4491,21493,117543,710021,4266279,28107745,
%T 196120515,1397747525,10648637151,84304440685,688868927151,
%U 5913133211249,52348170504555,479326416322933,4557380168574135,44560107679838549,449806788855058407,4680686977970550721
%N A000110 / A014182: (A154107 convolved with A014182 = Bell numbers).
%C A000110 / A014182 = (the eigensequence of Pascal's triangle) /
%C (eigensequence of the inverse of Pascal's triangle).
%C A014182 = expansion of exp(1-x-exp(-x)).
%F A000110 / A014182 = (1, 1, 2, 5, 15, 52, 203,...) / (1, 0, -1, 1, 2, -9, 9, 50,...).
%e A000110 = 52 = (1, 1, 3, 5, 15, 61) convolved with (1, 0, -1, 1, 2, -9)
%e = (61 - 5 + 3 + 2 - 9)
%t 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 *)
%Y Cf. A000110, A014182.
%K nonn
%O 0,3
%A _Gary W. Adamson_, Jan 04 2009
%E a(12) corrected and more terms added from _Vaclav Kotesovec_, Jul 26 2021
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