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A081566
Second binomial transform of expansion of exp(3cosh(x)).
1
1, 2, 7, 26, 118, 572, 3127, 18146, 114793, 765602, 5463982, 40870436, 323326813, 2667777842, 23092966267, 207651618746, 1947316349278, 18906249136892, 190564801592107, 1982986181092226, 21345005629846213, 236628248493001202
OFFSET
0,2
COMMENTS
Binomial transform of A081565.
LINKS
FORMULA
E.g.f.: exp(2*x) * exp(3*cosh(x))/e^3 = exp(3*cosh(x)+2*x-3).
MAPLE
seq(coeff(series(exp(3*cosh(x)+2*x-3), x, n+1)*factorial(n), x, n), n = 0 .. 30); # G. C. Greubel, Aug 13 2019
MATHEMATICA
With[{nn = 30}, CoefficientList[Series[Exp[3 Cosh[x] + 2 x - 3], {x, 0, nn}], x] Range[0, nn]!] (* Vincenzo Librandi, Aug 08 2013 *)
PROG
(PARI) my(x='x+O('x^30)); Vec(serlaplace( exp(3*cosh(x)+2*x-3) )) \\ G. C. Greubel, Aug 13 2019
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(3*Cosh(x)+2*x-3) )); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Aug 13 2019
(Sage) [factorial(n)*( exp(3*cosh(x)+2*x-3) ).series(x, n+1).list()[n] for n in (0..30)] # G. C. Greubel, Aug 13 2019
CROSSREFS
Sequence in context: A309396 A218670 A302691 * A213094 A141203 A346749
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 22 2003
STATUS
approved