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A118396 Eigenvector of triangle A118394; E.g.f.: exp( Sum_{n>=0} x^(3^n) ). 3


%S 1,1,1,7,25,61,481,2731,10417,454105,4309921,23452111,592433161,

%T 6789801877,46254009985,893881991731,11548704851041,93501748795441,

%U 4828847934591937,83867376656907415,823025819684123641,33409213329178701421,640457721676922946721

%N Eigenvector of triangle A118394; E.g.f.: exp( Sum_{n>=0} x^(3^n) ).

%C 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) ).

%H Alois P. Heinz, <a href="/A118396/b118396.txt">Table of n, a(n) for n = 0..450</a>

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

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

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

%p end:

%p seq(a(n), n=0..25); # _Alois P. Heinz_, Oct 01 2017

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

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

%K nonn

%O 0,4

%A _Paul D. Hanna_, May 07 2006

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Last modified February 22 17:35 EST 2019. Contains 320400 sequences. (Running on oeis4.)