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A081559 Expansion of e.g.f.: exp(cosh(2*x)), even powers only. 3
1, 4, 64, 1984, 97024, 6713344, 615829504, 71654785024, 10243143368704, 1755968011239424, 354197952894337024, 82788022987201183744, 22140953727834378993664, 6703959915806302859689984 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Periodic zeros suppressed.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..100

FORMULA

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

MAPLE

seq(coeff(series(exp(cosh(2*x)-1), x, 2*n+1)*factorial(2*n), x, 2*n), n = 0 .. 15); # G. C. Greubel, Aug 13 2019

MATHEMATICA

With[{nn = 30}, CoefficientList[Series[Exp[Cosh[2*x]-1], {x, 0, nn}], x] Range[0, nn]!][[1 ;; ;; 2]] (* G. C. Greubel, Aug 13 2019 *)

PROG

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

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

(Sage) [factorial(2*n)*( exp(cosh(2*x)-1) ).series(x, 2*n+1).list()[2*n] for n in (0..15)] # G. C. Greubel, Aug 13 2019

CROSSREFS

Cf. A005046, A081560.

Sequence in context: A301583 A181398 A326274 * A298433 A261042 A002454

Adjacent sequences:  A081556 A081557 A081558 * A081560 A081561 A081562

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Mar 22 2003

STATUS

approved

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Last modified October 13 16:50 EDT 2019. Contains 327968 sequences. (Running on oeis4.)