A260503 Coefficients in an asymptotic expansion of sequence A003319.

1, -2, -1, -5, -32, -253, -2381, -25912, -319339, -4388949, -66495386, -1100521327, -19751191053, -382062458174, -7924762051957, -175478462117633, -4132047373455024, -103115456926017761, -2718766185148876961, -75529218928863243200, -2205316818199975235447

Offset: 0

Author

Vaclav Kotesovec, Jul 27 2015

Keywords

• sign

Examples

			A003319(n) / n! ~ 1 - 2/n - 1/n^2 - 5/n^3 - 32/n^4 - 253/n^5 - 2381/n^6 - ...
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..420

Crossrefs

Cf. A003319, A259472, A261214, A261239, A261253, A261254.

Cf. A256168, A260491, A260530, A260532, A260578.

Programs

Mathematica

Flatten[{1, Table[Sum[Assuming[Element[x,Reals], SeriesCoefficient[E^(2/x)*x^2 / ExpIntegralEi[1/x]^2,{x,0,k}]] * StirlingS2[n-1,k-1], {k,1,n}], {n,1,20}]}] (* Vaclav Kotesovec, Aug 03 2015 *)

Formula

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

For n>0, Sum_{k=1..n} a(k) * Stirling1(n-1, k-1) = A259472(n). - Vaclav Kotesovec, Aug 03 2015

For n>0, a(n) = Sum_{k=1..n} A259472(k) * Stirling2(n-1, k-1). - Vaclav Kotesovec, Aug 03 2015