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A081558 Second binomial transform of expansion of exp(cosh(x)), A005046. 2
1, 2, 5, 14, 44, 152, 575, 2354, 10379, 48902, 245240, 1301984, 7294589, 42959282, 265263185, 1712168654, 11528506124, 80783015192, 588097479635, 4439382164114, 34699233959759, 280381494540182, 2339287666524440, 20125268756209664, 178348602246900569 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of A081557.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

FORMULA

E.g.f.: exp(2*x) * exp(cosh(x))/e = exp(cosh(x)+2*x-1).

MAPLE

seq(coeff(series(exp(cosh(x)+2*x-1), x, n+1)*factorial(n), x, n), n = 0 .. 30); # G. C. Greubel, Aug 13 2019

MATHEMATICA

With[{nn = 30}, CoefficientList[Series[Exp[Cosh[x] + 2 x - 1], {x, 0, nn}], x] Range[0, nn]!] (* Vincenzo Librandi, Aug 08 2013 *)

PROG

(PARI) my(x='x+O('x^30)); Vec(serlaplace( exp(cosh(x)+2*x-1) )) \\ G. C. Greubel, Aug 13 2019

(MAGMA) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(Cosh(x)+2*x-1) )); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Aug 13 2019

(Sage) [factorial(n)*( exp(cosh(x)+2*x-1) ).series(x, n+1).list()[n] for n in (0..30)] # G. C. Greubel, Aug 13 2019

CROSSREFS

Sequence in context: A118929 A287252 A204064 * A202059 A014322 A095148

Adjacent sequences:  A081555 A081556 A081557 * A081559 A081560 A081561

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Mar 22 2003

STATUS

approved

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Last modified October 15 07:42 EDT 2019. Contains 328026 sequences. (Running on oeis4.)