OFFSET
0,2
COMMENTS
Diagonal sums of number triangle A116395.
Diagonal sums of the Riordan matrix ((1-sqrt(1-4*x))/(2*x*sqrt(1-4*x)),(1-sqrt(1-4*x))/(2*sqrt(1-4*x))) (A035324). - Emanuele Munarini, Apr 26 2011
FORMULA
a(n) = Sum_{k=0..floor(n/2)} (4^(n-k)/2^k)*Sum_{j=0..k} C(k,j)*C(n-k+(j-1)/2,n-k)*(-1)^(k-j).
D-finite with recurrence: +2*n*a(n) +(-13*n+10)*a(n-1) +(9*n-16)*a(n-2) +2*(19*n-41)*a(n-3) +(23*n-66)*a(n-4) +2*(2*n-7)*a(n-5)=0. - R. J. Mathar, Jan 24 2020
MATHEMATICA
CoefficientList[Series[(x+(2+x)Sqrt[1-4x])/(2-6x-8x^2-2x^3), {x, 0, 25}], x] (* Emanuele Munarini, Apr 26 2011 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Feb 12 2006
STATUS
approved