A260530 Coefficients in asymptotic expansion of sequence A051296.

1, 2, 7, 35, 216, 1575, 13243, 126508, 1359437, 16312915, 217277446, 3194459333, 51557948291, 908431129702, 17376289236947, 358847480175063, 7959468559605624, 188702262366570387, 4760773506835189975, 127312428854513811012, 3596091234340397964321

Offset

0,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..132

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

Formula

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

Example

A051296(n) / n! ~ 1 + 2/n + 7/n^2 + 35/n^3 + 216/n^4 + 1575/n^5 + 13243/n^6 + ...

Mathematica

nmax = 30; b = CoefficientList[Assuming[Element[x, Reals], Series[E^(2/x)*x^2 / (ExpIntegralEi[1/x] - 2*x*E^(1/x))^2, {x, 0, nmax}]], x]; Flatten[{1, Table[Sum[b[[k+1]]*StirlingS2[n-1, k-1], {k, 1, n}], {n, 1, nmax}]}] (* Vaclav Kotesovec, Aug 03 2015 *)

Crossrefs

Cf. A051296, A256168, A260491, A260503, A260532, A260578.

Sequence in context: A043546 A350309 A307441 * A201690 A080831 A006947

Adjacent sequences: A260527 A260528 A260529 * A260531 A260532 A260533

Keyword

nonn

Author

Vaclav Kotesovec, Jul 28 2015

Status

approved