A274571 Column 0 of triangle A274570.

1, 1, 7, 127, 4377, 245481, 20391523, 2354116899, 360734454993, 70865037282673, 17367953099244051, 5195706189463681299, 1863485648739527246569, 789370246456579516316121, 389929989984983783920348611, 222178771969671609391720410691, 144648509476124539709343154760897, 106712830948451223242311469280356609, 88557950557114913966623605248882438755, 82132537612235618834557329353828430430755

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).

Links

• Paul D. Hanna, Table of n, a(n) for n = 0..40

Crossrefs

Cf. A274570, A274572, A274573, A274574.

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 A274570: */
for(n=0,10,for(k=0,n,print1(T(n,k),", "));print(""))
/* Print this sequence, which is column 0 */
for(n=0,20,print1(T(n,0),", "))