A219358 G.f. satisfies: A(x) = Sum_{n>=0} n! * x^n * A(x)^(n*(n-1)/2).

1, 1, 2, 8, 46, 334, 2882, 28604, 320248, 3993184, 54942740, 828086732, 13586200504, 241294019584, 4615319816192, 94629675177320, 2070911506927360, 48185049542009248, 1187816429730925424, 30923773410431125424, 847808674826433774928, 24414218135569507213312

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

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} n!*x^n * B(x)^(n*(n+1)/2) and is the g.f. of A219359.

Example

 G.f.: A(x) = 1 + x + 2*x^2 + 8*x^3 + 46*x^4 + 334*x^5 + 2882*x^6 +...
where
A(x) = 1 + 1!*x + 2!*x^2*A(x) + 3!*x^3*A(x)^3 + 4!*x^4*A(x)^6 + 5!*x^5*A(x)^10 + 6!*x^6*A(x)^15 +...

Prog

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

Crossrefs

Cf. A155804, A219359.

Sequence in context: A145844 A005840 A161881 * A088791 A111552 A321965

Adjacent sequences: A219355 A219356 A219357 * A219359 A219360 A219361

Keyword

nonn

Author

Paul D. Hanna, Nov 18 2012

Status

approved