OFFSET
0,3
REFERENCES
J. Riordan, Combinatorial Identities, Wiley, 1968, p. 77.
LINKS
FORMULA
From G. C. Greubel, Aug 14 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)*((171*x^2 - 90*x + 8)*sqrt(1 - 6*x) + (54*x^3 - 648*x^2 + 114*x - 8))*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 14 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 14 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Dec 08 2001
STATUS
approved