OFFSET
0,4
REFERENCES
J. Riordan, Combinatorial Identities, Wiley, 1968, p. 77.
LINKS
FORMULA
a(n) = 6*binomial(n, 3)*(1/2)_{n}*2^n*hypergeometric1f1(3-n, -2*n, 2), where (a)_{n} is the Pochhammer symbol. - G. C. Greubel, Aug 15 2017
G.f.: (90*x^3/(1-x)^7)*hypergeometric2f0(4,7/2; - ; 2*x/(1-x)^2). - G. C. Greubel, Aug 16 2017
a(n) ~ 2^(n + 1/2) * n^(n+3) / exp(n-1). - Vaclav Kotesovec, Jun 09 2019
MATHEMATICA
Join[{0, 0, 0}, Table[6*Binomial[n, 3]*Pochhammer[1/2, n]*2^n* Hypergeometric1F1[3-n, -2*n, 2], {n, 3, 50}]] (* G. C. Greubel, Aug 15 2017 *)
CoefficientList[Series[(90*t^3/(1-t)^7)*HypergeometricPFQ[{4, 7/2}, {}, 2*t/(1-t)^2], {t, 0, 50}], t] (* G. C. Greubel, Aug 16 2017 *)
PROG
(PARI) for(n=0, 50, print1(sum(k=0, n-3, ((n+k+3)!/(2^(k+3)*k!*(n-k-3)!))), ", ")) \\ G. C. Greubel, Aug 15 2017
(Magma) [0, 0, 0] cat [(&+[Binomial(n-3, k)*Factorial(n+k+3)/(2^(k+3) * Factorial(n-3)): k in [0..n-3]]): n in [3..30]]; // G. C. Greubel, Sep 23 2023
(SageMath)
def A065950(n): return sum(binomial(n-3, k)*rising_factorial(n-2, k+6)//2^(k+3) for k in range(n-2))
[A065950(n) for n in range(31)] # G. C. Greubel, Sep 23 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Dec 08 2001
STATUS
approved