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A274571 Column 0 of triangle A274570. 5
1, 1, 7, 127, 4377, 245481, 20391523, 2354116899, 360734454993, 70865037282673, 17367953099244051, 5195706189463681299, 1863485648739527246569, 789370246456579516316121, 389929989984983783920348611, 222178771969671609391720410691, 144648509476124539709343154760897, 106712830948451223242311469280356609, 88557950557114913966623605248882438755, 82132537612235618834557329353828430430755 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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..40

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 0 */

for(n=0, 20, print1(T(n, 0), ", "))

CROSSREFS

Cf. A274570, A274572, A274573, A274574.

Sequence in context: A215066 A092676 A002067 * A138523 A034670 A020516

Adjacent sequences:  A274568 A274569 A274570 * A274572 A274573 A274574

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jun 28 2016

STATUS

approved

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Last modified October 18 02:23 EDT 2019. Contains 328135 sequences. (Running on oeis4.)