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URL: https://oeis.org/A218003

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A218003
Number of degree-n permutations of order a power of 3.
3
1, 1, 1, 3, 9, 21, 81, 351, 1233, 46089, 434241, 2359611, 27387801, 264333213, 1722161169, 16514298711, 163094452641, 1216239520401, 50883607918593, 866931703203699, 8473720481213481, 166915156382509221, 2699805625227141201, 28818706120636531023, 439756550972215638129, 6766483260087819272601, 77096822666547068590401, 406859605390184444341678251
OFFSET
0,4
COMMENTS
Differs from A053499 first at n=27. - Alois P. Heinz, Jan 25 2014
LINKS
FORMULA
E.g.f.: exp( Sum_{n>=0} x^(3^n)/3^n ).
EXAMPLE
E.g.f.: A(x) = 1 + x + x^2/2! + 3*x^3/3! + 9*x^4/4! + 21*x^5/5! + 81*x^6/6! +...
where
log(A(x)) = x + x^3/3 + x^9/9 + x^27/27 + x^81/81 +...+ x^3^n/3^n +...
MAPLE
a:= proc(n) option remember; `if`(n<0, 0, `if`(n=0, 1,
add(mul(n-i, i=1..3^j-1)*a(n-3^j), j=0..ilog[3](n))))
end:
seq(a(n), n=0..30); # Alois P. Heinz, Jan 25 2014
MATHEMATICA
a[n_] := a[n] = If[n < 0, 0, If[n == 0, 1, Sum[Product[n-i, {i, 1, 3^j-1}]*a[n-3^j], {j, 0, Floor@Log[3, n]}]]];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Apr 28 2025, after Alois P. Heinz *)
PROG
(PARI) {a(n)=n!*polcoeff(exp(sum(k=0, ceil(log(n+1)/log(3)), x^(3^k)/3^k)+x*O(x^n)), n)}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
Sequence in context: A001470 A118932 A053499 * A146909 A146248 A074000
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 17 2012
STATUS
approved