A260949 Coefficients in asymptotic expansion of sequence A259871.

1, 4, 16, 76, 416, 2576, 17840, 137268, 1170104, 11050940, 115885968, 1353366864, 17640817784, 256630492660, 4153220868128, 74315436120300, 1458541231513152, 31131651836906752, 716862465409883040, 17683184383300077828, 464519709712796199816

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 A345889 A057725

Adjacent sequences: A260946 A260947 A260948 * A260950 A260951 A260952

Keyword

nonn

Author

Vaclav Kotesovec, Aug 05 2015

Status

approved