A080527 - OEIS

A080527

Expansion of e.g.f. exp(3*cosh(x))/e^3 (even powers only).

1, 3, 30, 543, 14745, 546618, 26119965, 1547467743, 110507211390, 9310580616243, 910032696123645, 101790848712790218, 12883623878563854105, 1827803943114479006043, 288318381606931126782270, 50215020818975432279332743, 9597691024295026236008687265

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OFFSET

0,2

COMMENTS

Periodic zeros suppressed.

LINKS

Table of n, a(n) for n=0..16.

FORMULA

E.g.f.: exp(3*cosh(x)-3).

a(0) = 1; a(n) = 3 * Sum_{k=1..n} binomial(2*n-1,2*k-1) * a(n-k). - Ilya Gutkovskiy, Mar 10 2022

EXAMPLE

exp(3*cosh(x))/exp(3) = 1 + 3*x^2/2! + 30*x^4/4! + ...

MATHEMATICA

With[{nn=30}, Take[CoefficientList[Series[Exp[3Cosh[x]]/E^3, {x, 0, nn}], x] Range[0, nn]!, {1, -1, 2}]] (* Harvey P. Dale, Dec 15 2013 *)

CROSSREFS

Cf. A000807, A005046, A081565.

Sequence in context: A370910 A377554 A375871 * A370057 A300617 A365653

Adjacent sequences: A080524 A080525 A080526 * A080528 A080529 A080530

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Mar 22 2003

STATUS

approved