A259607 G.f. satisfies: A(x) = 1+x + x^2 * A'(x)^2 / A(x)^2.

1, 1, 1, 2, 9, 66, 646, 7760, 109585, 1771810, 32211854, 649833996, 14399543754, 347618918364, 9080945744920, 255239884317292, 7680997048377377, 246417820289930866, 8395878803694101510, 302786064773642534220, 11523127939987785101646, 461518291638811484923036

Offset

0,4

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..350

Formula

a(n) ~ c * 2^n * (n-1)!, where c = 0.09202081821632249728460... . - Vaclav Kotesovec, Jul 10 2015

Example

G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 9*x^4 + 66*x^5 + 646*x^6 + 7760*x^7 +...
The logarithmic derivative begins:
A'(x)/A(x) = 1 + x + 4*x^2 + 29*x^3 + 286*x^4 + 3478*x^5 + 49750*x^6 + 813949*x^7 +...+ A182356(n)*x^n +...
where
A'(x)^2/A(x)^2 = 1 + 2*x + 9*x^2 + 66*x^3 + 646*x^4 + 7760*x^5 +...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+x + x^2*(A')^2/A^2 +x*O(x^n)); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A182356.

Sequence in context: A228696 A042255 A152213 * A214930 A089471 A196193

Adjacent sequences: A259604 A259605 A259606 * A259608 A259609 A259610

Keyword

nonn

Author

Paul D. Hanna, Jul 05 2015

Status

approved