A274574 - OEIS

%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