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A260532 Coefficients in asymptotic expansion of sequence A051295. 9
1, 2, 7, 31, 165, 1025, 7310, 59284, 543702, 5618267, 65200918, 846462826, 12229783811, 195394019337, 3427472046792, 65526442181293, 1355785469986828, 30166624979467869, 717769036033944699, 18174105506247664633, 487655384740384445407, 13816406622559942660420 (list; graph; refs; listen; history; text; internal format)
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

Cf. A051295, A134378, A256168, A260491, A260503, A260530, A260578.

Sequence in context: A227119 A002872 A105216 * A193657 A007164 A321208

Adjacent sequences:  A260529 A260530 A260531 * A260533 A260534 A260535

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Jul 28 2015

STATUS

approved

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Last modified November 22 08:46 EST 2019. Contains 329389 sequences. (Running on oeis4.)