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%I #30 Aug 05 2015 05:29:03
%S -1,1,-1,2,-1,9,26,201,1407,11714,107983,1102433,12332994,150103585,
%T 1974901951,27935229074,422799610943,6818164335881,116717210194218,
%U 2113959805887881,40388891717569887,811833598825134258,17126091132964548335,378335451153341591041
%N 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).
%H Eric M. Schmidt, <a href="/A259872/b259872.txt">Table of n, a(n) for n = 0..300</a>
%H Richard J. Martin, and Michael J. Kearney, <a href="http://dx.doi.org/10.1007/s00493-014-3183-3">Integral representation of certain combinatorial recurrences</a>, Combinatorica: 35:3 (2015), 309-315.
%F Martin and Kearney (2015) give a g.f.
%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
%t 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 *)
%o (Sage)
%o @CachedFunction
%o 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
%Y Cf. A259869, A259870, A259871, A260950, A052186.
%K sign,easy
%O 0,4
%A _N. J. A. Sloane_, Jul 09 2015
%E Definition corrected by and more terms from _Eric M. Schmidt_, Jul 10 2015
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