A234302 E.g.f. satisfies: A(x) = Sum_{n>=0} Product_{k=1..n} Integral A(x)^k dx.

1, 1, 3, 18, 170, 2240, 38378, 816946, 20935010, 631121324, 21994715164, 874082596116, 39179495872048, 1963122168878428, 109138409453801828, 6689677277646519704, 449643740848072663512, 32984171327232883654144, 2629601502882284005506808, 226977691912707098997408056

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! + 18*x^3/3! + 170*x^4/4! + 2240*x^5/5! +...
where
A(x) = 1 + [Integral A(x) dx] + [Integral A(x) dx]*[Integral A(x)^2 dx] + [Integral A(x) dx]*[Integral A(x)^2 dx]*[Integral A(x)^3 dx] +...
Related series:
A(x)^2 = 1 + 2*x + 8*x^2/2! + 54*x^3/3! + 538*x^4/4! + 7260*x^5/5! +...
A(x)^3 = 1 + 3*x + 15*x^2/2! + 114*x^3/3! + 1212*x^4/4! + 16950*x^5/5! +...
A(x)^4 = 1 + 4*x + 24*x^2/2! + 204*x^3/3! + 2324*x^4/4! + 33920*x^5/5! +...
A(x)^5 = 1 + 5*x + 35*x^2/2! + 330*x^3/3! + 4030*x^4/4! + 61620*x^5/5! +...
A(x)^6 = 1 + 6*x + 48*x^2/2! + 498*x^3/3! + 6510*x^4/4! + 104460*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^k+x*O(x^n))))); n!*polcoeff(A, n)}
for(n=0, 25, print1(a(n), ", "))

Crossrefs

Cf. A234303.

Sequence in context: A121423 A074932 A101483 * A099716 A352649 A113130

Adjacent sequences: A234299 A234300 A234301 * A234303 A234304 A234305

Keyword

nonn

Author

Paul D. Hanna, Dec 22 2013

Status

approved