OFFSET
0,2
FORMULA
a(n) ~ 12^(12*n + 1/4) / (2^(1/4) * Gamma(1/4) * 11^(11*n + 1/4) * n^(3/4)).
From Seiichi Manyama, Aug 16 2025: (Start)
Sum_{k=0..n} a(k) * a(n-k) = A169961(n).
G.f.: 1/sqrt(1 - 12*x*g^11) where g = 1+x*g^12.
G.f.: sqrt( g/(12-11*g) ) where g = 1+x*g^12. (End)
MATHEMATICA
nmax = 20; self = ConstantArray[0, nmax + 1]; self[[1]] = 1; self[[2]] = 6; Do[self[[k+1]] = (Binomial[12*k, k] - Sum[self[[j+1]]*self[[k - j + 1]], {j, 1, k-1}]) / (2*self[[1]]); , {k, 2, nmax}]; self
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Jun 07 2025
STATUS
approved
