OFFSET
0,4
COMMENTS
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
KEYWORD
nonn
AUTHOR
Paul D. Hanna, May 07 2006
STATUS
approved