A082135 Expansion of e.g.f. x*exp(4*x)*cosh(x).

0, 1, 8, 51, 304, 1765, 10104, 57239, 321248, 1787337, 9864040, 54035707, 294031632, 1590368429, 8556082136, 45812239455, 244255416256, 1297362967441, 6867617339592, 36243304518083, 190746485895920, 1001394643462773

Offset: 0

Author

Paul Barry, Apr 06 2003

Keywords

• easy
• nonn

Comments

Binomial transform of A082134. 4th 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 (16,-94,240,-225).

Crossrefs

Cf. A082133, A082136.

Programs

Magma

[n*(3^(n-1)+5^(n-1))/2: n in [0..30]]; // G. C. Greubel, Feb 05 2018

Mathematica

With[{nn = 20}, CoefficientList[Series[x Exp[4*x] Cosh[x], {x, 0, nn}], x] Range[0, nn]!] (* T. D. Noe, Dec 10 2012 *)
Table[n*(3^(n-1)+5^(n-1))/2, {n,0,30}] (* G. C. Greubel, Feb 05 2018 *)
LinearRecurrence[{16,-94,240,-225},{0,1,8,51},40] (* Harvey P. Dale, Sep 13 2024 *)

PARI

for(n=0,30, print1(n*(3^(n-1)+5^(n-1))/2, ", ")) \\ G. C. Greubel, Feb 05 2018

Formula

a(n) = n*(3^(n-1) + 5^(n-1))/2.

E.g.f.: x*exp(4x)*cosh(x).

G.f.: x*(17*x^2-8*x+1) / ((3*x-1)^2*(5*x-1)^2). [Colin Barker, Dec 10 2012]