OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
Let G(x) = (1-3*x)/(2*(x-1)*x) + (I*(1-2*x))/(2*x*sqrt(4*x-1)) with Im(x) > 0, then a(n) = [x^n] G(x). The generating function G(x) satisfies the differential equation 6*x^3 - 4*x + 1 = (8*x^5 - 22*x^4 + 21*x^3 - 8*x^2 + x)*diff(G(x), x) + (4*x^4 - 14*x^3 + 17*x^2 - 8*x + 1)*G(x).
a(n) = A212382(2*n, n). - Alois P. Heinz, May 03 2019
MAPLE
aList := proc(len) local gf, ser; assume(Im(x) > 0);
gf := (1-3*x)/(2*(x-1)*x) + (I*(1-2*x))/(2*x*sqrt(4*x-1));
ser := series(gf, x, len+2):
seq(coeff(ser, x, n), n=0..len) end: aList(27);
MATHEMATICA
Table[Binomial[2n, n+1] + 1, {n, 0, 26}]
PROG
(Magma) [Binomial(2*n, n+1) + 1: n in [0..30]]; // G. C. Greubel, Dec 26 2021
(Sage) [binomial(2*n, n+1) + 1 for n in (0..30)] # G. C. Greubel, Dec 26 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Peter Luschny, Feb 12 2019
STATUS
approved