A328006 Expansion of e.g.f. 1 / (1 - Sum_{k>=1} binomial(2*k,k) * x^k / (k + 1)!).

1, 1, 4, 23, 174, 1642, 18596, 245737, 3711294, 63056858, 1190408544, 24720216578, 560011664724, 13743710272060, 363241612472368, 10286092411744025, 310694791014710206, 9971177817032175594, 338830529059491098336, 12153453467291303419246, 458873804279349884222364

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Formula

E.g.f.: 1 / (2 - exp(2*x) * (BesselI(0,2*x) - BesselI(1,2*x))).

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * A000108(k) * a(n-k).

a(n) ~ n! / (exp(2*r)*(BesselI(0, 2*r) - BesselI(2, 2*r)) * r^(n+1)), where r = 0.52970787846036422338310218180536596363570735225100094676866... is the root of the equation exp(2*r)*(BesselI(0,2*r) - BesselI(1,2*r)) = 2. - Vaclav Kotesovec, Oct 02 2019

Maple

seq(n!*coeff(series(1/(2 - exp(2*x) * (BesselI(0, 2*x) - BesselI(1, 2*x))), x, 21), x, n), n = 0..20); # Vaclav Kotesovec, Oct 02 2019

Mathematica

nmax = 20; CoefficientList[Series[1/(2 - Exp[2 x] (BesselI[0, 2 x] - BesselI[1, 2 x])), {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] CatalanNumber[k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 20}]

Crossrefs

Cf. A000108, A001700, A088218, A178955, A304788, A328004.

Sequence in context: A084357 A360868 A075729 * A127131 A083355 A141763

Adjacent sequences: A328003 A328004 A328005 * A328007 A328008 A328009

Keyword

nonn

Author

Ilya Gutkovskiy, Oct 01 2019

Status

approved