

A211898


G.f.: exp( Sum_{n>=1} (2^n  (1)^n)^n * x^n/n ).


1



1, 3, 9, 261, 13419, 7867287, 10444212819, 84955235950827, 2235017786095822257, 273416315791427558035965, 125533366255776787874473759857, 242979442003484538229530424638338553, 1852958949086213206247388599213928431454549
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OFFSET

0,2


COMMENTS

CONJECTURE: the highest power of 3 dividing a(n) equals 3^A089792(n) for n>=0; that is, n!*a(n)/3^n is an integer not divisible by 3 for n>=0.
Given g.f. A(x), note that A(x)^(1/3) is not an integer series.


LINKS

Table of n, a(n) for n=0..12.


FORMULA

a(n) == 3 (mod 6) for n>0.


EXAMPLE

G.f.: A(x) = 1 + 3*x + 9*x^2 + 261*x^3 + 13419*x^4 + 7867287*x^5 +...
such that
log(A(x)) = 3*x + 3^2*x^2/2 + 9^3*x^3/3 + 15^4*x^4/4 + 33^5*x^5/5 + 63^6*x^6/6 + 129^7*x^7/7 + 255^8*x^8/8 +...+ (2^n  (1)^n)^n*x^n/n +...


PROG

(PARI) {a(n)=polcoeff(exp(sum(k=1, n, (2^k(1)^k)^k*x^k/k)+x*O(x^n)), n)}
for(n=0, 20, print1(a(n), ", "))


CROSSREFS

Cf. A211897, A155200, A089792.
Sequence in context: A091409 A027891 A073889 * A318970 A132516 A328125
Adjacent sequences: A211895 A211896 A211897 * A211899 A211900 A211901


KEYWORD

nonn


AUTHOR

Paul D. Hanna, Apr 25 2012


STATUS

approved



