A085387 E.g.f exp(x)*cosh(x+x^2/2).

1, 1, 2, 7, 23, 71, 242, 925, 3649, 14593, 61082, 269039, 1220375, 5658823, 27047386, 133453429, 674644673, 3482517185, 18399534386, 99518837527, 549283557463, 3088289136391, 17697783668930, 103351677649037, 614068613826689

Offset: 0

Author

Paul Barry, Jun 27 2003

Keywords

• easy
• nonn

Comments

Binomial transform of A085386. A085387 is the mean of A005425 and the sequence with e.g.f. exp(-x^2/2).

Crossrefs

Cf. A001147.

Programs

Mathematica

CoefficientList[Series[E^x*Cosh[x+x^2/2], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 19 2013 *)

Formula

E.g.f.: exp(x)*cosh(x+x^2/2).

Conjecture: a(n) -3*a(n-1) +2*a(n-2) +(-2*n+3)*a(n-3) +-(n-3)^2*a(n-4) +(n-3)*(n-4)*a(n-5)=0. - R. J. Mathar, Nov 24 2012

a(n) ~ 2^(-3/2) * exp(2*sqrt(n) - n/2 - 1) * n^(n/2) * (1+5/(6*sqrt(n))). - Vaclav Kotesovec, Oct 19 2013