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Self-convolution cube-root of column 2 (A127129) of triangle A127126.
7

%I #7 Jan 28 2020 22:29:16

%S 1,1,5,36,336,3793,49691,736301,12130141,219488417,4322334090,

%T 91974793971,2102457339356,51377007363853,1336508757460743,

%U 36876168645675673,1075680625224925835,33076997985647151025

%N Self-convolution cube-root of column 2 (A127129) of triangle A127126.

%H G. C. Greubel, <a href="/A127132/b127132.txt">Table of n, a(n) for n = 0..80</a>

%t T[n_, k_]:= T[n, k]= If[k==n, 1, Coefficient[(1 +x*Sum[x^(r-k-1)*Sum[T[r, c], {c,k+1,r}], {r,k+1,n}] +x^(n+1))^(k+1), x, n-k]]; CoefficientList[Series[ (Sum[T[n, 2]*x^n, {n,0,22}]/x^2)^(1/3), {x,0,20}], x] (* _G. C. Greubel_, Jan 28 2020 *)

%Y Cf. A127126, A127127, A127128, A127129, A127130, A127131, A127133, A127134, A127135.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Jan 05 2007