A259870 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).

0, 1, 1, 2, 5, 17, 74, 401, 2609, 19802, 171437, 1664585, 17892938, 210771761, 2698597601, 37301188610, 553473138677, 8773014886289, 147928235322314, 2643635547262049, 49909639472912177, 992516629078846010, 20736210820909594109, 454084963076923193321

Offset

0,4

Links

Colin Barker, Table of n, a(n) for n = 0..450

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 + 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

Mathematica

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 *)

Prog

(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

Crossrefs

Cf. A259869, A259871, A259872, A260948.

Sequence in context: A081046 A000774 A260948 * A348878 A118100 A129591

Adjacent sequences: A259867 A259868 A259869 * A259871 A259872 A259873

Keyword

nonn,easy

Author

N. J. A. Sloane, Jul 09 2015

Status

approved