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A153732 Binomial transform of A109747. 2
1, 3, 8, 19, 41, 84, 171, 347, 690, 1385, 2825, 5438, 11077, 24535, 33720, 102623, 350605, -1120228, 5876775, 11232063, -256532422, 1748895117, -4057110163, -42841409122, 605093026361 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Equals triple binomial transform of A014182.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..500

FORMULA

A007318 * A109747.

E.g.f.: exp(2*x+1-exp(-x)) = 1+3*x+8*x^2/2!+19*x^3/3!+....

a(n) = exp(1)*sum {k >= 0}(-1)^k*(2-k)^n/k!. Cf. A126617. - Peter Bala, Oct 28 2011.

G.f.: (G(0) - 1)/(x-1) where G(k) =  1 - 1/(1+k*x-2*x)/(1-x/(x-1/G(k+1) )); (recursively defined continued fraction). - Sergei N. Gladkovskii, Jan 17 2013

EXAMPLE

a(3) = 19 = (1, 3, 3, 1) dot (1, 2, 3, 3) = (1 + 6 + 9 + 3); where A109747 = (1, 2, 3, 3, 2, 3, 5, -4, 5, 55, -212,...).

MATHEMATICA

Join[{1}, Rest[CoefficientList[Series[Exp[2*x + 1 - Exp[-x]], {x, 0, 50}], x]*Range[0, 50]!]] (* G. C. Greubel, Aug 31 2016 *)

CROSSREFS

Cf. A109747, A014182, A126617.

Sequence in context: A260547 A182818 A095846 * A089924 A293947 A178457

Adjacent sequences:  A153729 A153730 A153731 * A153733 A153734 A153735

KEYWORD

sign

AUTHOR

Gary W. Adamson, Dec 31 2008

STATUS

approved

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Last modified October 23 14:06 EDT 2018. Contains 316528 sequences. (Running on oeis4.)