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A317170 Expansion of e.g.f. exp(exp(x) - 1)*BesselI(1,2*(exp(x) - 1))/(exp(x) - 1). 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Stirling transform of the Motzkin numbers (A001006).

LINKS

Table of n, a(n) for n=0..24.

N. J. A. Sloane, Transforms

Eric Weisstein's World of Mathematics, Stirling Transform

FORMULA

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

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}]

CROSSREFS

Cf. A001006, A064856, A086672, A317169.

Sequence in context: A192399 A233162 A186185 * A127087 A113060 A186374

Adjacent sequences:  A317167 A317168 A317169 * A317171 A317172 A317173

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jul 23 2018

STATUS

approved

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Last modified October 26 06:11 EDT 2020. Contains 338027 sequences. (Running on oeis4.)