A260948 Coefficients in asymptotic expansion of sequence A259870.

1, 2, 5, 17, 74, 395, 2526, 19087, 168603, 1723065, 20148031, 266437102, 3938754720, 64391209604, 1152961464743, 22424127879610, 470399253269776, 10579865622308851, 253840801521314095, 6468953273455413674, 174452533187403980841, 4962228907578051232358

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 A348878 A118100

Adjacent sequences: A260945 A260946 A260947 * A260949 A260950 A260951

Keyword

nonn

Author

Vaclav Kotesovec, Aug 05 2015

Status

approved