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

1, 1, 1, 7, 25, 61, 481, 2731, 10417, 454105, 4309921, 23452111, 592433161, 6789801877, 46254009985, 893881991731, 11548704851041, 93501748795441, 4828847934591937, 83867376656907415, 823025819684123641, 33409213329178701421, 640457721676922946721

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

Mathematica

a[n_] := a[n] = If[n==0, 1, Sum[Function[j, j! a[n-j] Binomial[n-1, j-1]][3^i], {i, 0, Log[3, n]}]];
a /@ Range[0, 25] (* Jean-François Alcover, Nov 07 2020, after Alois P. Heinz *)

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: A372371 A344560 A118395 * A330044 A193375 A362523

Adjacent sequences: A118393 A118394 A118395 * A118397 A118398 A118399

Keyword

nonn

Author

Paul D. Hanna, May 07 2006

Status

approved