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A089468 Hyperbinomial transform of A089467 and also the 2nd hyperbinomial transform of A089466. 2
1, 3, 15, 110, 1083, 13482, 203569, 3618540, 74058105, 1715620148, 44384718879, 1268498827752, 39692276983555, 1349678904881400, 49556966130059553, 1954156038072106448, 82363978221026323761, 3695194039210436996400 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
See A088956 for the definition of the hyperbinomial transform.
LINKS
FORMULA
a(n) = sum(k=0, n, (n-k+1)^(n-k-1)*C(n, k)*A089467(k)). a(n) = sum(k=0, n, 2*(n-k+2)^(n-k-1)*C(n, k)*A089466(k)). a(n) = sum(m=0, n, sum(j=0, m, C(m, j)*C(n, n-m-j)*(n+1)^(n-m-j)*(m+j)!/(-2)^j)/m!)).
E.g.f.: (LambertW(-x)^2*exp(-1/2*LambertW(-x)^2))/(x^2*(1+LambertW(-x))). - Vladeta Jovovic, Oct 26 2004
a(n) ~ exp(3/2)*n^n. - Vaclav Kotesovec, Jul 09 2013
MATHEMATICA
CoefficientList[Series[(LambertW[-x]^2*E^(-1/2*LambertW[-x]^2))/(x^2*(1+LambertW[-x])), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jul 09 2013 *)
PROG
(PARI) a(n)=if(n<0, 0, sum(m=0, n, sum(j=0, m, binomial(m, j)*binomial(n, n-m-j)*(n+1)^(n-m-j)*(m+j)!/(-2)^j)/m!))
CROSSREFS
Sequence in context: A054201 A090355 A083483 * A109498 A142967 A360864
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 08 2003
STATUS
approved

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Last modified March 28 14:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)