cp's OEIS Frontend

A274572 Column 1 of triangle A274570.

%I A274572 #8 Jun 24 2017 01:05:34
%S A274572 1,2,20,470,19912,1326382,127677580,16767030632,2880746218304,
%T A274572 627213971899610,168767535712912684,54994347890521005100,
%U A274572 21342142821229037730064,9726400286221416303901358,5143644030714149522751534524,3124088412968372614077895431788,2159818183532141245447039295746240,1686295004858842334963772859214802354,1476540037893212558044217633785452773068,1440964034588041764141738802548853847618732
%N A274572 Column 1 of triangle A274570.
%C A274572 Triangle A274570 transforms diagonals in the array A274390 of coefficients of successive iterations of Euler's tree function (A000169).
%H A274572 Paul D. Hanna, <a href="/A274572/b274572.txt">Table of n, a(n) for n = 0..39</a>
%o A274572 (PARI) {T(n, k)=local(F=x,
%o A274572 LW=serreverse(x*exp(-x+x*O(x^(n+2)))), M, N, P, m=max(n, k));
%o A274572 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 A274572 N=matrix(m+1, m+1, r, c, M[r, c]);
%o A274572 P=matrix(m+1, m+1, r, c, M[r+1, c]);
%o A274572 (n-k)!*(P~*N~^-1)[n+1, k+1]}
%o A274572 /* Print triangle A274570: */
%o A274572 for(n=0,10,for(k=0,n,print1(T(n,k),", "));print(""))
%o A274572 /* Print this sequence, which is column 1 */
%o A274572 for(n=0,20,print1(T(n+1,1),", "))
%Y A274572 Cf. A274570, A274571, A274573, A274574.
%K A274572 nonn
%O A274572 0,2
%A A274572 _Paul D. Hanna_, Jun 28 2016