|
%I #30 Aug 05 2015 05:22:44
%S 0,1,1,2,5,17,74,401,2609,19802,171437,1664585,17892938,210771761,
%T 2698597601,37301188610,553473138677,8773014886289,147928235322314,
%U 2643635547262049,49909639472912177,992516629078846010,20736210820909594109,454084963076923193321
%N a(0)=0, a(1)=1; a(n) = n*a(n-1) + (n-2)*a(n-2) - Sum_{j=1..n-1} a(j)*a(n-j).
%H Colin Barker, <a href="/A259870/b259870.txt">Table of n, a(n) for n = 0..450</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 + 5/n^2 + 17/n^3 + 74/n^4 + 395/n^5 + 2526/n^6 + 19087/n^7 + 168603/n^8 + 1723065/n^9 + 20148031/n^10), for coefficients see A260948. - _Vaclav Kotesovec_, Jul 29 2015
%t nmax = 25; CoefficientList[Assuming[Element[x, Reals], Series[-1/(ExpIntegralEi[1 + 1/x]/Exp[1 + 1/x] - 1) - 1, {x, 0, nmax}]], x] (* _Vaclav Kotesovec_, Aug 05 2015 *)
%o (PARI) a=vector(30); a[1]=0; a[2]=1; for(n=2, #a-1, a[n+1] = n*a[n] + (n-2)*a[n-1] - sum(j=1, n-1, a[j+1]*a[n-j+1])); a \\ _Colin Barker_, Jul 09 2015
%Y Cf. A259869, A259871, A259872, A260948.
%K nonn,easy
%O 0,4
%A _N. J. A. Sloane_, Jul 09 2015
|
