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A274572 Column 1 of triangle A274570. 5


%S 1,2,20,470,19912,1326382,127677580,16767030632,2880746218304,

%T 627213971899610,168767535712912684,54994347890521005100,

%U 21342142821229037730064,9726400286221416303901358,5143644030714149522751534524,3124088412968372614077895431788,2159818183532141245447039295746240,1686295004858842334963772859214802354,1476540037893212558044217633785452773068,1440964034588041764141738802548853847618732

%N Column 1 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="/A274572/b274572.txt">Table of n, a(n) for n = 0..39</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 1 */

%o for(n=0,20,print1(T(n+1,1),", "))

%Y Cf. A274570, A274571, A274573, A274574.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jun 28 2016

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Last modified November 18 10:18 EST 2019. Contains 329261 sequences. (Running on oeis4.)