A134381 Row sums of triangle A134380.

1, 2, 5, 15, 52, 205, 921, 4766, 28685, 201159, 1630840, 15071725, 156331161, 1794763970, 22548418541, 307236496071, 4507944378004, 70813851019717, 1185225078743601, 21049903662123422, 395303080572770549, 7825181077750155999, 162835332607069248760

Offset: 0

Author

Gary W. Adamson, Oct 22 2007

Keywords

• nonn

Examples

			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, ...).
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..150

Crossrefs

Cf. A134380, A051295.

Programs

Mathematica

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 *)

Formula

Binomial transform of A051295.

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

a(n) ~ exp(1) * (n-1)!. - Vaclav Kotesovec, Feb 06 2015

Extensions

More terms from Vaclav Kotesovec, Feb 06 2015