OFFSET
0,2
LINKS
Francesc Fite, Kiran S. Kedlaya, Victor Rotger and Andrew V. Sutherland, Sato-Tate distributions and Galois endomorphism modules in genus 2, arXiv preprint arXiv:1110.6638 [math.NT], 2011-2012 (the sequence c-hat in Section 5.1.1).
FORMULA
a(n) = Sum_{k=0..n} binomial(n, k)*2^(n-k)*c(k)^2, where c() = A126120().
Conjecture: (n+2)^2*a(n) +2*(-3*n^2-5*n-1)*a(n-1) -4*(n-1)*(n-5)*a(n-2) +24*(n-1)*(n-2)*a(n-3)=0. - R. J. Mathar, Dec 04 2013 [ Maple's sumrecursion command applied to the above formula for a(n) produces this recurrence. - Peter Bala, Jul 06 2015 ]
a(n) ~ 2^(n-1) * 3^(n+3) / (Pi * n^3). - Vaclav Kotesovec, Jul 20 2019
MAPLE
MATHEMATICA
b[n_] := Coefficient[(x^2+1)^n, x, n]; (* A126869 *)
c[n_] := b[n]/(n/2+1); (* A126120 *)
ch[n_] := Sum[Binomial[n, k] 2^(n-k) c[k]^2, {k, 0, n}]; (* A202856 *)
Table[ch[n], {n, 0, 30}] (* Jean-François Alcover, Aug 10 2018, translated from Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Dec 25 2011
STATUS
approved