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A260948 Coefficients in asymptotic expansion of sequence A259870. 5
1, 2, 5, 17, 74, 395, 2526, 19087, 168603, 1723065, 20148031, 266437102, 3938754720, 64391209604, 1152961464743, 22424127879610, 470399253269776, 10579865622308851, 253840801521314095, 6468953273455413674, 174452533187403980841, 4962228907578051232358 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..21.

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

FORMULA

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

EXAMPLE

A259870(n)/((n-1)!/exp(1)) ~ 1 + 2/n + 5/n^2 + 17/n^3 + 74/n^4 + 395/n^5 + ...

MATHEMATICA

nmax = 25; b = CoefficientList[Assuming[Element[x, Reals], Series[x/(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. A259870, A260578, A260949, A260950.

Sequence in context: A112831 A081046 A000774 * A259870 A118100 A129591

Adjacent sequences:  A260945 A260946 A260947 * A260949 A260950 A260951

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Aug 05 2015

STATUS

approved

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Last modified November 19 16:06 EST 2019. Contains 329320 sequences. (Running on oeis4.)