A155805 E.g.f. satisfies: A(x) = Sum_{n>=0} x^n/n! * A(x)^(n(n+1)/2).

1, 1, 3, 19, 191, 2656, 47392, 1034335, 26721781, 798018616, 27058991246, 1027237384009, 43172232488959, 1990253576425960, 99871804451808040, 5419775866582473211, 316301430225674131433, 19756213549154356027408

Offset

0,3

Links

Table of n, a(n) for n=0..17.

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*(n-1)/2) and is the e.g.f. of A155804.

Example

E.g.f.: A(x) = 1 + x + 3*x^2/2! + 19*x^3/3! + 191*x^4/4! + 2656*x^5/5! +...
where e.g.f. A(x) satisfies:
A(x) = 1 + x*A(x) + x^2/2!*A(x)^3 + x^3/3!*A(x)^6 + x^4/4!*A(x)^10 +...
Let B(x) = A(x/B(x)) be the e.g.f. of A155804 then:
B(x) = 1 + x + x^2/2!*B(x) + x^3/3!*B(x)^3 + x^4/4!*B(x)^6 + x^5/5!*B(x)^10 +...
B(x) = 1 + x + x^2/2! + 4*x^3/3! + 19*x^4/4! + 161*x^5/5! + 1606*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)/2)/k!+x*O(x^n))); n!*polcoeff(A, n)}

Crossrefs

Cf. A155804, A155806, A155807, A107591, A219359.

Sequence in context: A090354 A119394 A101481 * A218261 A001517 A080893

Adjacent sequences: A155802 A155803 A155804 * A155806 A155807 A155808

Keyword

nonn

Author

Paul D. Hanna, Jan 27 2009

Status

approved