OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..400
FORMULA
a(n) = Sum_{m=0..n} A130757(n,m), n>=0, with A130757(n,m) = n!*2^(n-m) *(-1)^m*binomial(n+1/2,n-m)/m!, n>=m>=0, else 0.
Conjecture: a(n) +2*(1-2*n)*a(n-1) +2*(2*n-1)*(n-1)*a(n-2)=0. - R. J. Mathar, Oct 02 2013
MATHEMATICA
T[n_, k_]:= (-1)^k*n!*2^(n-k)*Binomial[n +1/2, n-k]/k!; Table[Sum[T[n, k], {k, 0, n}], {n, 0, 40}] (* G. C. Greubel, May 14 2018 *)
PROG
(PARI) for(n=0, 30, print1(sum(k=0, n, (-1)^k*n!*2^(n-k)*binomial(n+1/2, n-k)/k!), ", ")) \\ G. C. Greubel, May 14 2018
(Magma) [Round(Factorial(n)*(&+[(-1)^k*2^(n-k)*Gamma(n+3/2)/(Gamma(k+1) *Gamma(n -k+1)*Gamma(k+3/2)): k in [0..n]])): n in [0..20]]; // G. C. Greubel, May 14 2018
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Wolfdieter Lang, Aug 07 2007
STATUS
approved