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A200313
E.g.f. satisfies: A(x) = exp(x^3*A(x)^3/3!).
3
1, 1, 70, 28000, 33833800, 91842150400, 471920698849600, 4105733038511104000, 55918460253906250000000, 1124922893768186370457600000, 31962429471680921191680301600000, 1237813985055170041194334820761600000, 63474917512551971525535771981021376000000
OFFSET
0,3
LINKS
FORMULA
a(n) = (3*n+1)^(n-1) * (3*n)!/(n!*(3!)^n).
E.g.f.: (1/x)*Series_Reversion( x*exp(-x^3/3!) ).
Powers of e.g.f.: define a(n,m) by A(x)^m = Sum_{n>=0} a(n,m)*x^(3*n)/(3*n)!
then a(n,m) = m*(3*n+m)^(n-1) * (3*n)!/(n!*(3!)^n).
EXAMPLE
E.g.f.: A(x) = 1 + x^3/3! + 70*x^6/6! + 28000*x^9/9! + 33833800*x^12/12! + ...
where log(A(x)) = x^3*A(x)^3/3! and
A(x)^3 = 1 + 3*x^3/3! + 270*x^6/6! + 120960*x^9/9! + 155925000*x^12/12! + ...
MATHEMATICA
Table[(3*n + 1)^(n - 1)*(3*n)!/(n!*(3!)^n), {n, 0, 30}] (* G. C. Greubel, Jul 27 2018 *)
PROG
(PARI) {a(n)=(3*n)!*polcoeff(1/x*serreverse(x*(exp(-x^3/3!+x*O(x^(3*n))))), 3*n)}
(PARI) {a(n)=(3*n+1)^(n-1)*(3*n)!/(n!*(3!)^n)}
(Magma) [(3*n+1)^(n-1)*Factorial(3*n)/(6^n*Factorial(n)): n in [0..30]]; // G. C. Greubel, Jul 27 2018
(GAP) List([0..10], n->(3*n+1)^(n-1)*Factorial(3*n)/(Factorial(n)*Factorial(3)^n)); # Muniru A Asiru, Jul 28 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 15 2011
STATUS
approved