A200313 E.g.f. satisfies: A(x) = exp(x^3*A(x)^3/3!).

1, 1, 70, 28000, 33833800, 91842150400, 471920698849600, 4105733038511104000, 55918460253906250000000, 1124922893768186370457600000, 31962429471680921191680301600000, 1237813985055170041194334820761600000, 63474917512551971525535771981021376000000

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..100

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

Cf. A025035, A034941, A200314, A200315.

Sequence in context: A177638 A274646 A005983 * A177642 A177644 A146499

Adjacent sequences: A200310 A200311 A200312 * A200314 A200315 A200316

Keyword

nonn

Author

Paul D. Hanna, Nov 15 2011

Status

approved