A259872 a(0)=-1, a(1)=1; a(n) = n*a(n-1) + (n-2)*a(n-2) + Sum_{j=1..n-1} a(j)*a(n-j) + 2*Sum_{j=0..n-1} a(j)*a(n-1-j).

-1, 1, -1, 2, -1, 9, 26, 201, 1407, 11714, 107983, 1102433, 12332994, 150103585, 1974901951, 27935229074, 422799610943, 6818164335881, 116717210194218, 2113959805887881, 40388891717569887, 811833598825134258, 17126091132964548335, 378335451153341591041

Offset: 0

Author

N. J. A. Sloane, Jul 09 2015

Keywords

• sign
• easy

Links

• Eric M. Schmidt, Table of n, a(n) for n = 0..300
• Richard J. Martin, and Michael J. Kearney, Integral representation of certain combinatorial recurrences, Combinatorica: 35:3 (2015), 309-315.

Crossrefs

Cf. A259869, A259870, A259871, A260950, A052186.

Programs

Mathematica

nmax = 25; CoefficientList[Assuming[Element[x, Reals], Series[-1/(ExpIntegralEi[1 + 1/x]/Exp[1 + 1/x] + 1), {x, 0, nmax}]], x] (* Vaclav Kotesovec, Aug 05 2015 *)

Sage

@CachedFunction
def a(n) : return -1 if n==0 else 1 if n==1 else n*a(n-1) + (n-2)*a(n-2) + sum(a(j)*a(n-j) for j in [1..n-1]) + 2*sum(a(j)*a(n-1-j) for j in [0..n-1]) # Eric M. Schmidt, Jul 10 2015

Formula

Martin and Kearney (2015) give a g.f.

a(n) ~ (n-1)! / exp(1) * (1 - 2/n + 1/n^2 + 1/n^3 - 10/n^4 - 61/n^5 - 382/n^6 - 3489/n^7 - 39001/n^8 - 484075/n^9 - 6619449/n^10), for coefficients see A260950. - Vaclav Kotesovec, Jul 29 2015

Extensions

Definition corrected by and more terms from Eric M. Schmidt, Jul 10 2015