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A118396 Eigenvector of triangle A118394; E.g.f.: exp( Sum_{n>=0} x^(3^n) ). 3
1, 1, 1, 7, 25, 61, 481, 2731, 10417, 454105, 4309921, 23452111, 592433161, 6789801877, 46254009985, 893881991731, 11548704851041, 93501748795441, 4828847934591937, 83867376656907415, 823025819684123641, 33409213329178701421, 640457721676922946721 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

E.g.f. of triangle A118394 is: exp(x+y*x^3), where A118394(n,k) = n!/k!/(n-3*k)!. More generally, given a triangle with e.g.f.: exp(x+y*x^b), the eigenvector will have e.g.f.: exp( Sum_{n>=0} x^(b^n) ).

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..450

FORMULA

a(n) = Sum_{k=0..[n/3]} n!/k!/(n-3*k)! *a(k) for n>=0, with a(0)=1.

MAPLE

a:= proc(n) option remember; `if`(n=0, 1, add((j-> j!*

      a(n-j)*binomial(n-1, j-1))(3^i), i=0..ilog[3](n)))

    end:

seq(a(n), n=0..25);  # Alois P. Heinz, Oct 01 2017

PROG

(PARI) {a(n)=n!*polcoeff(exp(sum(k=0, ceil(log(n+1)/log(3)), x^(3^k))+x*O(x^n)), n)}

CROSSREFS

Cf. A118394, A118395; variants: A118393, A118932.

Sequence in context: A098538 A033814 A118395 * A193375 A185787 A299273

Adjacent sequences:  A118393 A118394 A118395 * A118397 A118398 A118399

KEYWORD

nonn

AUTHOR

Paul D. Hanna, May 07 2006

STATUS

approved

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Last modified February 21 21:41 EST 2018. Contains 299427 sequences. (Running on oeis4.)