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A218003 Number of degree-n permutations of order a power of 3. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 23 14:29 EDT 2019. Contains 328345 sequences. (Running on oeis4.)