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A260949 Coefficients in asymptotic expansion of sequence A259871. 5
1, 4, 16, 76, 416, 2576, 17840, 137268, 1170104, 11050940, 115885968, 1353366864, 17640817784, 256630492660, 4153220868128, 74315436120300, 1458541231513152, 31131651836906752, 716862465409883040, 17683184383300077828, 464519709712796199816 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

Richard J. Martin, and Michael J. Kearney, Integral representation of certain combinatorial recurrences, Combinatorica: 35:3 (2015), 309-315.

FORMULA

a(k) ~ 4 * exp(-1) * (k-1)! / (log(2))^k.

EXAMPLE

A259871(n)/((n-1)!/exp(1)) ~ 1 + 4/n + 16/n^2 + 76/n^3 + 416/n^4 + 2576/n^5 + ...

MATHEMATICA

nmax = 25; b = CoefficientList[Assuming[Element[x, Reals], Series[x/(2*ExpIntegralEi[1 + 1/x]/Exp[1 + 1/x] - 1)^2, {x, 0, nmax+1}]], x]; Table[Sum[b[[k+1]]*StirlingS2[n, k-1], {k, 1, n+1}], {n, 0, nmax}]

CROSSREFS

Cf. A259871, A260578, A260948, A260950.

Sequence in context: A241023 A200725 A255906 * A049426 A057725 A196192

Adjacent sequences:  A260946 A260947 A260948 * A260950 A260951 A260952

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Aug 05 2015

STATUS

approved

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Last modified May 7 06:18 EDT 2021. Contains 343636 sequences. (Running on oeis4.)