OFFSET
0,3
REFERENCES
J. Riordan, Combinatorial Identities, Wiley, 1968, p. 77.
LINKS
FORMULA
From G. C. Greubel, Aug 15 2017: (Start)
a(n) = 4*n*(n - 1)*(1/2)_{n}*(-6)^(n - 2)* hypergeometric1f1(2 - n; -2*n; -2/3), where (a)_{n} is the Pochhammer symbol.
E.g.f.: (-1/81)*(1 + 6*x)^(-5/2)*((-99*x^2 - 54*x - 4)*sqrt(1 + 6*x) + (-54*x^3 + 66*x + 4))*exp(-(1 - sqrt(1 + 6*x))/3). (End)
G.f.: (6*x^2/(1-x)^5)*hypergeometric2f0(3,5/2; - ; -6*x/(1-x)^2). - G. C. Greubel, Aug 16 2017
MATHEMATICA
Join[{0, 0}, Table[4*n*(n - 1)*Pochhammer[1/2, n]*(-6)^(n - 2)* Hypergeometric1F1[2 - n, -2*n, -2/3], {n, 2, 50}]] (* G. C. Greubel, Aug 15 2017 *)
PROG
(PARI) for(n=0, 50, print1(sum(k=0, n-2, ((n+k+2)!/(4*k!*(n-k-2)!))*(-3/2)^k ), ", ")) \\ G. C. Greubel, Aug 15 2017
CROSSREFS
KEYWORD
sign
AUTHOR
N. J. A. Sloane, Dec 08 2001
STATUS
approved