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

0,2

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 A379685

Adjacent sequences: A080524 A080525 A080526 * A080528 A080529 A080530

Keyword

easy,nonn

Author

Paul Barry, Mar 22 2003

Status

approved