OFFSET
0,4
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.
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
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 *)
PROG
(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
CROSSREFS
KEYWORD
sign,easy
AUTHOR
N. J. A. Sloane, Jul 09 2015
EXTENSIONS
Definition corrected by and more terms from Eric M. Schmidt, Jul 10 2015
STATUS
approved