A207493 E.g.f. A(x) is the series reversion of 2*x-1/2*x^2-exp(x)+1.

1, 2, 13, 141, 2141, 41798, 997340, 28124253, 915095222, 33744966795, 1390772973547, 63353273661835, 3160751396077900, 171405094563763674, 10038777321831260503, 631498191927510881178, 42464602911622645539047, 3039724643022777390236243

Offset: 1

Author

Vladimir Kruchinin, Feb 18 2012

Keywords

• nonn

Crossrefs

Cf. A226571.

Programs

Mathematica

Rest[CoefficientList[InverseSeries[Series[2*x-1/2*x^2-E^x+1, {x, 0, 20}], x],x]*Range[0, 20]!] (* Vaclav Kotesovec, Jan 22 2014 *)

Maxima

a(n):=(sum((n+k-1)!*sum(1/(k-j)!*sum(1/l!*sum(((-1)^(i+l)*2^(l-2*i) *binomial(l,i)*stirling2(n+j-i-l-1,j-l))/(n+j-i-l-1)!, i,0,l), l,0,j), j,0,k), k,0,n-1));

Formula

a(n) = (sum(k=0..n-1, (n+k-1)!*sum(j=0..k, 1/(k-j)!*sum(l=0..j, 1/l!*sum(i=0..l, ((-1)^(i+l)*2^(l-2*i)* C(l,i)*stirling2(n+j-i-l-1,j-l))/(n+j-i-l-1)!))))).

a(n) ~ n^(n-1) / (sqrt(1+c) * exp(n) * (3-c*(2+c)/2)^(n-1/2)), where c = LambertW(exp(2)) = 1.5571455989976... (see A226571). - Vaclav Kotesovec, Jan 22 2014