A082136 Expansion of e.g.f. x*exp(5*x)*cosh(x).

0, 1, 10, 78, 560, 3880, 26400, 177632, 1185280, 7853184, 51699200, 338331136, 2201948160, 14258137088, 91894620160, 589744496640, 3770069811200, 24015941435392, 152494553825280, 965472423378944, 6096346179174400

Offset: 0

Author

Paul Barry, Apr 06 2003

Keywords

• easy
• nonn

Comments

Binomial transform of A082135. 5th binomial transform of (0,1,0,3,0,5,0,7,...)

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (20,-148,480,-576).

Crossrefs

Cf. A082134.

Programs

Magma

[n*(4^(n-1)+6^(n-1))/2: n in [0..30]]; // G. C. Greubel, Feb 05 2018

Mathematica

With[{nmax = 50}, CoefficientList[Series[x*Exp[5*x]*Cosh[x], {x, 0, nmax}], x]*Range[0, nmax]!] (* or *) Table[n*(4^(n-1)+6^(n-1))/2, {n,0,30}] (* G. C. Greubel, Feb 05 2018 *)

PARI

for(n=0,30, print1(n*(4^(n-1)+6^(n-1))/2, ", ")) \\ G. C. Greubel, Feb 05 2018

Formula

a(n) = n*(4^(n-1) + 6^(n-1))/2.

E.g.f.: x*exp(5*x)*cosh(x).

G.f. x*(1-10*x+26*x^2) / ( (6*x-1)^2*(4*x-1)^2 ). - R. J. Mathar, Nov 24 2012