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%I #5 Jul 02 2016 03:09:01
%S 1,2,39,2188,247465,47290506,13732594855,5645761143968,
%T 3124313624563281,2240929551882269890,2023001689428835457551,
%U 2245340983227461222262600,3005921392102922941037743561,4777188534537036418050441999458,8892651921874938986718539648539335,19167346139929272962512547586833106016,47363669252787891219004826832547428944065,133017373943189884985366059167726505579520322,421334607602498277189468756234637306051458074191,1495034827615578030423476599123008111000477082402040,5906697677063490360959940664316005473632429506949424681
%N Central terms of triangle A274570.
%C Triangle A274570 transforms diagonals in the array A274390 of coefficients of successive iterations of Euler's tree function (A000169).
%o (PARI) {T(n, k)=local(F=x,
%o LW=serreverse(x*exp(-x+x*O(x^(n+2)))), M, N, P, m=max(n, k));
%o M=matrix(m+3, m+3, r, c, F=x; for(i=1, r+c-2, F=subst(F, x, LW)); polcoeff(F, c));
%o N=matrix(m+1, m+1, r, c, M[r, c]);
%o P=matrix(m+1, m+1, r, c, M[r+1, c]);
%o (n-k)!*(P~*N~^-1)[n+1, k+1]}
%o /* Print triangle : */
%o for(n=0,10,for(k=0,n,print1(T(n,k),", "));print(""))
%o /* Print this sequence, which is central terms */
%o for(n=0,20,print1(T(2*n,n),", "))
%Y Cf. A274570, A274571, A274572, A274573.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Jun 28 2016
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