OFFSET
0,2
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..134
Richard J. Martin, and Michael J. Kearney, Integral representation of certain combinatorial recurrences, Combinatorica: 35:3 (2015), 309-315.
FORMULA
a(k) ~ 2 * (k-1)! / (log(2))^k.
a(n) = Sum_{k=0..n} A134378(k) * Stirling2(n, k). - Vaclav Kotesovec, Aug 04 2015
EXAMPLE
A051295(n)/(n-1)! ~ 1 + 2/n + 7/n^2 + 31/n^3 + 165/n^4 + 1025/n^5 + 7310/n^6 + ...
MATHEMATICA
nmax = 30; b = CoefficientList[Assuming[Element[x, Reals], Series[E^(2/x)*x / (ExpIntegralEi[1/x] - E^(1/x))^2, {x, 0, nmax+1}]], x]; Table[Sum[b[[k+1]] * StirlingS2[n, k-1], {k, 1, n+1}], {n, 0, nmax}] (* Vaclav Kotesovec, Aug 03 2015 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Jul 28 2015
STATUS
approved