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

Offset: 0

Author

Paul Barry, Mar 22 2003

Keywords

• easy
• nonn

Comments

Periodic zeros suppressed.

Examples

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

Crossrefs

Cf. A000807, A005046, A081565.

Programs

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 *)

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