A274574 Central terms of triangle A274570.

1, 2, 39, 2188, 247465, 47290506, 13732594855, 5645761143968, 3124313624563281, 2240929551882269890, 2023001689428835457551, 2245340983227461222262600, 3005921392102922941037743561, 4777188534537036418050441999458, 8892651921874938986718539648539335, 19167346139929272962512547586833106016, 47363669252787891219004826832547428944065, 133017373943189884985366059167726505579520322, 421334607602498277189468756234637306051458074191, 1495034827615578030423476599123008111000477082402040, 5906697677063490360959940664316005473632429506949424681

Offset: 0

Author

Paul D. Hanna, Jun 28 2016

Keywords

• nonn

Comments

Triangle A274570 transforms diagonals in the array A274390 of coefficients of successive iterations of Euler's tree function (A000169).

Crossrefs

Cf. A274570, A274571, A274572, A274573.

Programs

PARI

{T(n, k)=local(F=x,
LW=serreverse(x*exp(-x+x*O(x^(n+2)))), M, N, P, m=max(n, k));
M=matrix(m+3, m+3, r, c, F=x; for(i=1, r+c-2, F=subst(F, x, LW)); polcoeff(F, c));
N=matrix(m+1, m+1, r, c, M[r, c]);
P=matrix(m+1, m+1, r, c, M[r+1, c]);
(n-k)!*(P~*N~^-1)[n+1, k+1]}
/* Print triangle : */
for(n=0,10,for(k=0,n,print1(T(n,k),", "));print(""))
/* Print this sequence, which is central terms */
for(n=0,20,print1(T(2*n,n),", "))