A323721 Expansion of e.g.f. log(2*exp(x/2)*cosh(sqrt(5)*x/2) - 1).

0, 1, 2, -3, -6, 50, -13, -1498, 6234, 59145, -748678, -1415238, 92962179, -411570250, -11993577118, 167710062977, 1224967301754, -51920085859710, 135335259830867, 14992073315394822, -201575378391009366, -3667884891055854535, 128570113943360964602, 209758874692705861322

Offset

0,3

Links

Table of n, a(n) for n=0..23.

Formula

E.g.f.: log(1 + Sum_{k>=1} Lucas(k)*x^k/k!).

a(0) = 0; a(n) = Lucas(n) - (1/n)*Sum_{k=1..n-1} binomial(n,k)*Lucas(n-k)*k*a(k).

Maple

seq(n!*coeff(series(log(2*exp(x/2)*cosh(sqrt(5)*x/2)-1), x=0, 24), x, n), n=0..23); # Paolo P. Lava, Jan 28 2019

Mathematica

nmax = 23; CoefficientList[Series[Log[2 Exp[x/2] Cosh[Sqrt[5] x/2] - 1], {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = LucasL[n] - Sum[Binomial[n, k] LucasL[n - k] k a[k], {k, 1, n - 1}]/n; a[0] = 0; Table[a[n], {n, 0, 23}]

Crossrefs

Cf. A000032, A000204, A007553, A112005, A294222.

Sequence in context: A099411 A018372 A097350 * A277374 A062309 A018390

Adjacent sequences: A323718 A323719 A323720 * A323722 A323723 A323724

Keyword

sign

Author

Ilya Gutkovskiy, Jan 25 2019

Status

approved