A155807 E.g.f. satisfies: A(x) = Sum_{n>=0} x^n/n! * A(x)^(n(n+1)).

1, 1, 5, 55, 969, 23661, 741013, 28363707, 1284098609, 67149601273, 3984121444581, 264485848799679, 19426332734137849, 1564277403496216293, 137040382838351173301, 12977244383702330201731

Offset

0,3

Links

Table of n, a(n) for n=0..15.

Formula

E.g.f. satisfies: A(x) = B(x*A(x)) and A(x/B(x)) = B(x) where B(x) satisfies:

B(x) = Sum_{n>=0} x^n/n! * B(x)^(n^2) and is the e.g.f. of A155806.

Example

E.g.f.: A(x) = 1 + x + 5*x^2/2! + 55*x^3/3! + 969*x^4/4! + 23661*x^5/5! +...
where e.g.f. A(x) satisfies:
A(x) = 1 + x*A(x)^2 + x^2/2!*A(x)^6 + x^3/3!*A(x)^12 + x^4/4!*A(x)^20 +...
Let B(x) = A(x/B(x)) be the e.g.f. of A155806 then:
B(x) = 1 + x*B(x) + x^2/2!*B(x)^4 + x^3/3!*B(x)^9 + x^4/4!*B(x)^16 +...
B(x) = 1 + x + 3*x^2/2! + 22*x^3/3! + 269*x^4/4! + 4616*x^5/5! + 102847*x^6/6! +...

Prog

(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=1+sum(k=1, n, x^k*A^(k*(k+1))/k!+x*O(x^n))); n!*polcoeff(A, n)}

Crossrefs

Cf. A155804, A155805, A155806.

Sequence in context: A293013 A195513 A172493 * A135861 A141361 A203013

Adjacent sequences: A155804 A155805 A155806 * A155808 A155809 A155810

Keyword

nonn

Author

Paul D. Hanna, Jan 27 2009

Status

approved