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A305404 Expansion of Sum_{k>=0} (2*k - 1)!!*x^k/Product_{j=1..k} (1 - j*x). 2
1, 1, 4, 25, 217, 2416, 32839, 527185, 9761602, 204800551, 4801461049, 124402647370, 3529848676237, 108859319101261, 3625569585663484, 129689000146431205, 4958830249864725997, 201834650901695603296, 8712774828941647677019, 397596632650906687905565 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Stirling transform of A001147.

LINKS

Table of n, a(n) for n=0..19.

N. J. A. Sloane, Transforms

Eric Weisstein's World of Mathematics, Stirling Transform

FORMULA

E.g.f.: 1/sqrt(3 - 2*exp(x)).

a(n) = Sum_{k=0..n} Stirling2(n,k)*(2*k - 1)!!.

a(n) ~ sqrt(2/3) * n^n / ((log(3/2))^(n + 1/2) * exp(n)). - Vaclav Kotesovec, Jul 01 2018

MATHEMATICA

nmax = 19; CoefficientList[Series[Sum[(2 k - 1)!! x^k/Product[1 - j x, {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]

nmax = 19; CoefficientList[Series[1/Sqrt[3 - 2 Exp[x]], {x, 0, nmax}], x] Range[0, nmax]!

Table[Sum[StirlingS2[n, k] (2 k - 1)!!, {k, 0, n}], {n, 0, 19}]

CROSSREFS

Cf. A000670, A001147, A004123, A305405.

Sequence in context: A047733 A198198 A007830 * A218826 A060911 A060912

Adjacent sequences:  A305401 A305402 A305403 * A305405 A305406 A305407

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, May 31 2018

STATUS

approved

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Last modified February 21 22:10 EST 2020. Contains 332113 sequences. (Running on oeis4.)