OFFSET
0,3
REFERENCES
J. Riordan, Combinatorial Identities, Wiley, 1968, p. 77.
LINKS
FORMULA
From G. C. Greubel, Aug 14 2017: (Start)
a(n) = 2*n*(1/2)_{n}*(-4)^(n - 1)* hypergeometric1f1(1 - n, -2*n, -1).
E.g.f.: ((1 + 4*x)^(3/2) - 2*x*(1 + 4*x)^(1/2) - 1)* exp((sqrt(1 + 4*x) -1)/2)/(4*(1 + 4*x)^(3/2)). (End)
G.f.: (x/(1-x)^3)*hypergeometric2f0(2,3/2; - ; -4*x/(1-x)^2). - G. C. Greubel, Aug 16 2017
MATHEMATICA
Join[{0}, Table[2*n*Pochhammer[1/2, n]*(-4)^(n - 1)*Hypergeometric1F1[1 - n, -2*n, -1], {n, 1, 50}]] (* G. C. Greubel, Aug 14 2017 *)
PROG
(PARI) for(n=0, 50, print1(sum(k=0, n-1, (n+k+1)!/(2*(n-k-1)!*k!)), ", ")) \\ G. C. Greubel, Aug 14 2017
CROSSREFS
KEYWORD
sign
AUTHOR
N. J. A. Sloane, Dec 08 2001
STATUS
approved