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A274572
Column 1 of triangle A274570.
5
1, 2, 20, 470, 19912, 1326382, 127677580, 16767030632, 2880746218304, 627213971899610, 168767535712912684, 54994347890521005100, 21342142821229037730064, 9726400286221416303901358, 5143644030714149522751534524, 3124088412968372614077895431788, 2159818183532141245447039295746240, 1686295004858842334963772859214802354, 1476540037893212558044217633785452773068, 1440964034588041764141738802548853847618732
OFFSET
0,2
COMMENTS
Triangle A274570 transforms diagonals in the array A274390 of coefficients of successive iterations of Euler's tree function (A000169).
LINKS
PROG
(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 1 */
for(n=0, 20, print1(T(n+1, 1), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jun 28 2016
STATUS
approved