A200315 E.g.f. satisfies: A(x) = exp(x^5*A(x)^5/5!).

1, 1, 1386, 32288256, 4527372986136, 2373840824586206976, 3532226719132271834449776, 12455133709483299692008910094336, 91656142095228409912231665590704016256, 1280796898530759870923631204720457656538791936

Offset

0,3

Links

Table of n, a(n) for n=0..9.

Formula

a(n) = (5*n+1)^(n-1) * (5*n)! / (n!*(5!)^n).

E.g.f.: (1/x)*Series_Reversion( x*exp(-x^5/5!) ).

Powers of e.g.f.: define a(n,m) by A(x)^m = Sum_{n>=0} a(n,m)*x^(5*n)/(5*n)!

then a(n,m) = m*(5*n+m)^(n-1) * (5*n)!/(n!*(5!)^n).

Example

E.g.f.: A(x) = 1 + x^5/5! + 1386*x^10/10! + 32288256*x^15/15! +...
where log(A(x)) = x^5*A(x)^5/5! and
A(x)^5 = 1 + 5*x^5/5! + 9450*x^10/10! + 252252000*x^15/15! + 38192529375000*x^20/20! +...

Prog

(PARI) {a(n)=(5*n)!*polcoeff(1/x*serreverse(x*(exp(-x^5/5!+x*O(x^(5*n))))), 5*n)}
(PARI) {a(n)=(5*n+1)^(n-1)*(5*n)!/(n!*(5!)^n)}

Crossrefs

Cf. A034941, A200313, A200314.

Sequence in context: A214355 A230334 A295435 * A063879 A063172 A317972

Adjacent sequences: A200312 A200313 A200314 * A200316 A200317 A200318

Keyword

nonn

Author

Paul D. Hanna, Nov 15 2011

Status

approved