A218003 Number of degree-n permutations of order a power of 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

Alois P. Heinz, Table of n, a(n) for n = 0..200

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

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

Cf. A005388, A053499.

Sequence in context: A001470 A118932 A053499 * A146909 A146248 A074000

Adjacent sequences: A218000 A218001 A218002 * A218004 A218005 A218006

Keyword

nonn

Author

Paul D. Hanna, Oct 17 2012

Status

approved