A384695 Self-convolution square-root of A169961, where A169961(n) = binomial(12*n,n).
1, 6, 120, 2850, 72990, 1950816, 53594508, 1500996420, 42639593040, 1224606404670, 35477155257720, 1035058071490152, 30375294227227530, 895810786837337880, 26530164526824124560, 788575111385154710700, 23513904388397505712014, 703104985574123730695460, 21076207836773295148694400
Offset: 0
Keywords
Programs
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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
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)