A323667 Expansion of e.g.f. exp(BesselI(0,2*x) + BesselI(1,2*x) - 1).

1, 1, 3, 10, 43, 211, 1191, 7463, 51535, 386809, 3133273, 27184620, 251253157, 2461527511, 25459020289, 276987375642, 3160197122183, 37705878268985, 469340324930493, 6081394853597162, 81866045488063721, 1142928276326927223, 16521454311961005245, 246917508673451732077

Offset: 0

Author

Ilya Gutkovskiy, Jan 23 2019

Keywords

• nonn

Crossrefs

Cf. A001405, A302197, A304788.

Programs

Maple

seq(n!*coeff(series(exp(BesselI(0,2*x)+BesselI(1,2*x)-1),x=0,24),x,n),n=0..23); # Paolo P. Lava, Jan 28 2019

Mathematica

nmax = 23; CoefficientList[Series[Exp[BesselI[0, 2 x] + BesselI[1, 2 x] - 1], {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = Sum[Binomial[k, Floor[k/2]] Binomial[n - 1, k - 1] a[n - k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 23}]

PARI

my(x='x + O('x^25)); Vec(serlaplace(exp(besseli(0, 2*x)+x*besseli(1, 2*x)-1))) \\ Michel Marcus, Jan 24 2019

Formula

a(0) = 1; a(n) = Sum_{k=1..n} A001405(k)*binomial(n-1,k-1)*a(n-k).