A234303 E.g.f. satisfies: A(x) = Sum_{n>=0} Product_{k=1..n} Integral A(x)^(2*k-1) dx.

1, 1, 3, 21, 243, 4033, 88579, 2448797, 82364899, 3289214713, 153124779251, 8192660285429, 498079027659539, 34090100961715761, 2606369415952417187, 221123234953585638989, 20697146958115491545091, 2126375962641919801375721, 238685649016900987418110355, 29151156993731776756459644837

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Example

 E.g.f.: A(x) = 1 + x + 3*x^2/2! + 21*x^3/3! + 243*x^4/4! + 4033*x^5/5! +...
where
A(x) = 1 + [Integral A(x) dx] + [Integral A(x) dx]*[Integral A(x)^3 dx] + [Integral A(x) dx]*[Integral A(x)^3 dx]*[Integral A(x)^5 dx] +...
Related series:
A(x)^3 = 1 + 3*x + 15*x^2/2! + 123*x^3/3! + 1503*x^4/4! + 25239*x^5/5! +...
A(x)^5 = 1 + 5*x + 35*x^2/2! + 345*x^3/3! + 4635*x^4/4! + 81485*x^5/5! +...
A(x)^7 = 1 + 7*x + 63*x^2/2! + 735*x^3/3! + 10983*x^4/4! + 205891*x^5/5! +...
A(x)^9 = 1 + 9*x + 99*x^2/2! + 1341*x^3/3! + 22275*x^4/4! + 448857*x^5/5! +...

Prog

 (PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+sum(m=1, n, prod(k=1, m, intformal(A^(2*k-1)+x*O(x^n))))); n!*polcoeff(A, n)}
for(n=0, 25, print1(a(n), ", "))

Crossrefs

Cf. A234302.

Sequence in context: A367375 A058562 A145083 * A138213 A193333 A290129

Adjacent sequences: A234300 A234301 A234302 * A234304 A234305 A234306

Keyword

nonn

Author

Paul D. Hanna, Dec 22 2013

Status

approved