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A274571 Column 0 of triangle A274570.

%I A274571 #7 Jun 28 2016 18:26:58
%S A274571 1,1,7,127,4377,245481,20391523,2354116899,360734454993,
%T A274571 70865037282673,17367953099244051,5195706189463681299,
%U A274571 1863485648739527246569,789370246456579516316121,389929989984983783920348611,222178771969671609391720410691,144648509476124539709343154760897,106712830948451223242311469280356609,88557950557114913966623605248882438755,82132537612235618834557329353828430430755
%N A274571 Column 0 of triangle A274570.
%C A274571 Triangle A274570 transforms diagonals in the array A274390 of coefficients of successive iterations of Euler's tree function (A000169).
%H A274571 Paul D. Hanna, <a href="/A274571/b274571.txt">Table of n, a(n) for n = 0..40</a>
%o A274571 (PARI) {T(n, k)=local(F=x,
%o A274571 LW=serreverse(x*exp(-x+x*O(x^(n+2)))), M, N, P, m=max(n, k));
%o A274571 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 A274571 N=matrix(m+1, m+1, r, c, M[r, c]);
%o A274571 P=matrix(m+1, m+1, r, c, M[r+1, c]);
%o A274571 (n-k)!*(P~*N~^-1)[n+1, k+1]}
%o A274571 /* Print triangle A274570: */
%o A274571 for(n=0,10,for(k=0,n,print1(T(n,k),", "));print(""))
%o A274571 /* Print this sequence, which is column 0 */
%o A274571 for(n=0,20,print1(T(n,0),", "))
%Y A274571 Cf. A274570, A274572, A274573, A274574.
%K A274571 nonn
%O A274571 0,3
%A A274571 _Paul D. Hanna_, Jun 28 2016