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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Triangle A274570 transforms diagonals in the array A274390 of coefficients of successive iterations of Euler's tree function (A000169).

LINKS

Paul D. Hanna, Table of n, a(n) for n = 0..39

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

Cf. A274570, A274571, A274573, A274574.

Sequence in context: A188811 A009252 A210901 * A292396 A274738 A012816

Adjacent sequences:  A274569 A274570 A274571 * A274573 A274574 A274575

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jun 28 2016

STATUS

approved

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Last modified October 21 11:15 EDT 2019. Contains 328294 sequences. (Running on oeis4.)