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%I #8 Jun 24 2017 01:05:41
%S 1,3,39,1125,56505,4354923,476265591,70056231213,13329387478113,
%T 3184105899176739,932720103991595919,328710383679927689157,
%U 137188135970104212440721,66909975066823379752742835,37706189062081696231083478647,24312515006613477431766856702797,17784145956730483348850500758855969,14647274671009402833580157237962722147,13492886769176913829412675003231182928079
%N Column 2 of triangle A274570.
%C Triangle A274570 transforms diagonals in the array A274390 of coefficients of successive iterations of Euler's tree function (A000169).
%H Paul D. Hanna, <a href="/A274573/b274573.txt">Table of n, a(n) for n = 0..38</a>
%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 A274570: */
%o for(n=0,10,for(k=0,n,print1(T(n,k),", "));print(""))
%o /* Print this sequence, which is column 2 */
%o for(n=0,20,print1(T(n+2,2),", "))
%Y Cf. A274570, A274571, A274572, A274574.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Jun 28 2016
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