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A089468
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Hyperbinomial transform of A089467 and also the 2nd hyperbinomial transform of A089466.
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2
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1, 3, 15, 110, 1083, 13482, 203569, 3618540, 74058105, 1715620148, 44384718879, 1268498827752, 39692276983555, 1349678904881400, 49556966130059553, 1954156038072106448, 82363978221026323761, 3695194039210436996400
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OFFSET
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0,2
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COMMENTS
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See A088956 for the definition of the hyperbinomial transform.
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LINKS
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FORMULA
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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
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MATHEMATICA
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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 *)
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PROG
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(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!))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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