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%I #20 Sep 25 2024 04:11:22
%S 1,2,5,15,52,205,921,4766,28685,201159,1630840,15071725,156331161,
%T 1794763970,22548418541,307236496071,4507944378004,70813851019717,
%U 1185225078743601,21049903662123422,395303080572770549,7825181077750155999,162835332607069248760
%N Row sums of triangle A134380.
%H Vaclav Kotesovec, <a href="/A134381/b134381.txt">Table of n, a(n) for n = 0..150</a>
%F Binomial transform of A051295.
%F G.f.: (1 + x/((1-x)*S(0) - x))/(1-x), where S(k) = 1 - (k+1)*x/(1 - x - (k+1)*x/S(k+1)); (continued fraction). - _Sergei N. Gladkovskii_, Feb 05 2015
%F a(n) ~ exp(1) * (n-1)!. - _Vaclav Kotesovec_, Feb 06 2015
%e a(3) = 15 = (1, 3, 3, 1) dot (1, 1, 2, 5) = 1 + 3 + 6 + 5, where A051295 = (1, 1, 2, 5, 15, 54, 235, ...).
%t max = 20; Clear[g]; g[max + 2] = 1; g[k_] := g[k] = 1 - (k+1)*x/(1 - x - (k+1)*x/g[k+1]; gf = (1 + x/((1-x)*g[0] -x))/(1-x); CoefficientList[Series[gf, {x, 0, max}], x] (* _Vaclav Kotesovec_, Feb 06 2015, after _Sergei N. Gladkovskii_ *)
%Y Cf. A134380, A051295.
%K nonn
%O 0,2
%A _Gary W. Adamson_, Oct 22 2007
%E More terms from _Vaclav Kotesovec_, Feb 06 2015