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A305406 Expansion of Sum_{k>=0} binomial(2*k,k)*x^k/Product_{j=1..k} (1 - j*x). 2
1, 2, 8, 40, 234, 1544, 11242, 89016, 758504, 6900012, 66590782, 678322704, 7262393832, 81431657220, 953339019606, 11622207372104, 147199295291518, 1932876310310488, 26265519359529974, 368752956750812256, 5340795881536757632, 79691179458925839676, 1223524383429928039306 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Stirling transform of A000984.

LINKS

Table of n, a(n) for n=0..22.

N. J. A. Sloane, Transforms

Eric Weisstein's World of Mathematics, Stirling Transform

FORMULA

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

a(n) = Sum_{k=0..n} Stirling2(n,k)*binomial(2*k,k).

MATHEMATICA

nmax = 22; CoefficientList[Series[Sum[Binomial[2 k, k] x^k/Product[1 - j x, {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]

nmax = 22; CoefficientList[Series[Exp[2 (Exp[x] - 1)] BesselI[0, 2 (Exp[x] - 1)], {x, 0, nmax}], x] Range[0, nmax]!

Table[Sum[StirlingS2[n, k] Binomial[2 k, k], {k, 0, n}], {n, 0, 22}]

CROSSREFS

Cf. A000984, A064856.

Sequence in context: A089603 A209358 A116456 * A296050 A055882 A002301

Adjacent sequences:  A305403 A305404 A305405 * A305407 A305408 A305409

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, May 31 2018

STATUS

approved

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Last modified July 17 16:58 EDT 2019. Contains 325107 sequences. (Running on oeis4.)