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

0,2

Links

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

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

Example

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, ...).

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 *)

Crossrefs

Cf. A134380, A051295.

Sequence in context: A303924 A336021 A186001 * A107589 A249892 A352853

Adjacent sequences: A134378 A134379 A134380 * A134382 A134383 A134384

Keyword

nonn

Author

Gary W. Adamson, Oct 22 2007

Extensions

More terms from Vaclav Kotesovec, Feb 06 2015

Status

approved