A225109 E.g.f. (sin(3x) + cos x) / cos(4x).

1, 3, 15, 117, 1185, 15123, 230895, 4116837, 83860545, 1921996323, 48942778575, 1370953667157, 41893214676705, 1386843017916723, 49441928730798255, 1888542637550347077, 76946148390480577665, 3331009898404800736323, 152682246738275154625935, 7387240827905368219116597

Offset: 0

Author

M. F. Hasler, Apr 28 2013

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A006873, A007289, A007286.

Programs

Maple

per4 := proc(n) local j; 2*((1-I)/(1+I))^n*(1+add(binomial(n,j)* polylog(-j,I)*4^j, j=0..n)) end: A225109 := n -> Im(per4(n));
seq(A225109(i), i=0..11); # Peter Luschny, Apr 29 2013

Mathematica

mx = 17; Range[0, mx]! CoefficientList[ Series[ (Sin[3x] + Cos[x])/Cos[4x], {x, 0, mx}], x] (* Robert G. Wilson v, Apr 28 2013 *)

PARI

v=Vec((sin(3*x) + cos(x)) / cos(4*x)); vector(#v,i,v[i]*(i-1)!)

PARI

x='x+O('x^66); Vec(serlaplace((sin(3*x)+cos(x))/cos(4*x))) \\ Joerg Arndt, Apr 28 2013

Formula

a(n) = Im(2*((1-I)/(1+I))^n*(1+sum_{j=0..n}(binomial(n,j)*Li_{-j}(I)* 4^j))). - Peter Luschny, Apr 29 2013

a(n) ~ n! * sqrt(2+sqrt(2)) * 2^(3*n+1)/Pi^(n+1). - Vaclav Kotesovec, Jun 02 2013