A317170 Expansion of e.g.f. exp(exp(x) - 1)*BesselI(1,2*(exp(x) - 1))/(exp(x) - 1).

1, 1, 3, 11, 48, 242, 1374, 8619, 58923, 434595, 3431263, 28817120, 256100717, 2397920319, 23567078396, 242343368931, 2600148486462, 29036252825090, 336754427112094, 4048299252733563, 50357053778129599, 647129716643654763, 8579133975080008700, 117178742009906802080, 1646975673395621229201

Offset: 0

Author

Ilya Gutkovskiy, Jul 23 2018

Keywords

• nonn

Comments

Stirling transform of the Motzkin numbers (A001006).

Links

• N. J. A. Sloane, Transforms
• Eric Weisstein's World of Mathematics, Stirling Transform

Crossrefs

Cf. A001006, A064856, A086672, A317169.

Programs

Maple

a:=series(exp(exp(x) - 1)*BesselI(1,2*(exp(x) - 1))/(exp(x) - 1), x=0, 26): seq(n!*coeff(a, x, n), n=0..24); # Paolo P. Lava, Mar 26 2019

Mathematica

nmax = 24; CoefficientList[Series[Exp[Exp[x] - 1] BesselI[1, 2 (Exp[x] - 1)]/(Exp[x] - 1), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[StirlingS2[n, k] Hypergeometric2F1[(1 - k)/2, -k/2, 2, 4], {k, 0, n}], {n, 0, 24}]

Formula

a(n) = Sum_{k=0..n} Stirling2(n,k)*A001006(k).