A274573 Column 2 of triangle A274570.

1, 3, 39, 1125, 56505, 4354923, 476265591, 70056231213, 13329387478113, 3184105899176739, 932720103991595919, 328710383679927689157, 137188135970104212440721, 66909975066823379752742835, 37706189062081696231083478647, 24312515006613477431766856702797, 17784145956730483348850500758855969, 14647274671009402833580157237962722147, 13492886769176913829412675003231182928079

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..38

Crossrefs

Cf. A274570, A274571, A274572, 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 2 */
for(n=0,20,print1(T(n+2,2),", "))