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A134381 Row sums of triangle A134380. 2
1, 2, 5, 15, 52, 205, 921, 4766, 28685, 201159, 1630840, 15071725, 156331161, 1794763970, 22548418541, 307236496071, 4507944378004, 70813851019717, 1185225078743601, 21049903662123422, 395303080572770549, 7825181077750155999, 162835332607069248760 (list; graph; refs; listen; history; text; internal format)
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: A000110 A303924 A186001 * A107589 A249892 A006790

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

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Last modified October 21 08:27 EDT 2018. Contains 316405 sequences. (Running on oeis4.)