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A081444
Second binomial transform of expansion of cosh(sinh(x)).
2
1, 2, 5, 14, 45, 162, 641, 2718, 12249, 58370, 294493, 1571374, 8858053, 52542882, 326804185, 2122860862, 14366452913, 101063123202, 738075208501, 5587492946510, 43795838894941, 354876969914786, 2968890716640945
OFFSET
0,2
COMMENTS
Second binomial transform of A003709 (viewed as unsigned, with periodic zeros added).
Binomial transform of A081443.
LINKS
FORMULA
E.g.f.: exp(2*x) * cosh(sinh(x)).
MAPLE
seq(coeff(series(exp(2*x)*cosh(sinh(x)), x, n+1)*factorial(n), x, n), n = 0 .. 30); # G. C. Greubel, Aug 14 2019
MATHEMATICA
With[{nn = 30}, CoefficientList[Series[Exp[2x]Cosh[Sinh[x]], {x, 0, nn}], x] Range[0, nn]!] (* Vincenzo Librandi, Aug 08 2013 *)
PROG
(PARI) my(x='x+O('x^30)); Vec(serlaplace( exp(2*x)*cosh(sinh(x)) )) \\ G. C. Greubel, Aug 14 2019
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(2*x)*Cosh(Sinh(x)) )); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Aug 14 2019
(Sage) [factorial(n)*( exp(2*x)*cosh(sinh(x)) ).series(x, n+1).list()[n] for n in (0..30)] # G. C. Greubel, Aug 14 2019
CROSSREFS
Sequence in context: A149893 A149894 A030126 * A268004 A119429 A290615
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 22 2003
STATUS
approved