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A065980 Inverse binomial transform of [1^1,2^2,3^3,...], shifted right by one index. 1
1, 3, 20, 186, 2248, 33340, 585744, 11891236, 273854368, 7053523236, 200894140120, 6268924259884, 212691682554960, 7795165961244532, 306908654169113416, 12918649608270463740, 578931362074039774144 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
{0, a(n),n=1,...} = inverse binomial transform of {A001923(m), m=0,...} [From Tilman Neumann, Dec 17 2008]
LINKS
N. J. A. Sloane, Transforms
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
MATHEMATICA
CoefficientList[Series[-E^(-x)*LambertW[-x]/(1+LambertW[-x])^3/x, {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Feb 17 2014 *)
PROG
(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))
CROSSREFS
Sequence in context: A358214 A085390 A212789 * A302581 A305460 A073767
KEYWORD
easy,nonn
AUTHOR
Robert A. Stump (bee_ess107(AT)yahoo.com), Dec 09 2001
STATUS
approved

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Last modified March 28 04:13 EDT 2024. Contains 371235 sequences. (Running on oeis4.)