A065980 Inverse binomial transform of [1^1,2^2,3^3,...], shifted right by one index.

1, 3, 20, 186, 2248, 33340, 585744, 11891236, 273854368, 7053523236, 200894140120, 6268924259884, 212691682554960, 7795165961244532, 306908654169113416, 12918649608270463740, 578931362074039774144

Offset: 1

Author

Robert A. Stump (bee_ess107(AT)yahoo.com), Dec 09 2001

Keywords

• easy
• nonn

Comments

{0, a(n),n=1,...} = inverse binomial transform of {A001923(m), m=0,...} [From Tilman Neumann, Dec 17 2008]

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200
• F. Ellermann, Illustration of binomial transforms
• N. J. A. Sloane, Transforms

Crossrefs

Cf. A001923, A069856.

Programs

Mathematica

CoefficientList[Series[-E^(-x)*LambertW[-x]/(1+LambertW[-x])^3/x, {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Feb 17 2014 *)

PARI

a(n)=if(n<1,0,(n-1)!*polcoeff(exp(-x+O(x^n))*sum(k=0,n-1,(k+1)^(k+1)*x^k/k!),n-1))

Formula

O.g.f.: Sum_{n>0} (n*x/(1+x))^n. E.g.f.: int(-exp(-x)*LambertW(-x)/(1+LambertW(-x))^3/x, x). - Vladeta Jovovic, Apr 12 2003

a(n) ~ n^n * exp(-exp(-1)). - Vaclav Kotesovec, Feb 17 2014