A245307 G.f. satisfies: A(x) = A( x/A(x) )^2 / (1+x).

1, 1, 2, 10, 77, 771, 9258, 127656, 1969366, 33422650, 616779303, 12272428173, 261620716744, 5945330149226, 143439343672519, 3661506704040203, 98597706579694403, 2793561790527733313, 83084652845766283317, 2588418449175558698525, 84305591450606402889544

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Example

G.f.: A(x) = 1 + x + 2*x^2 + 10*x^3 + 77*x^4 + 771*x^5 + 9258*x^6 +...
Related expansions.
A(x)^2 = 1 + 2*x + 5*x^2 + 24*x^3 + 178*x^4 + 1736*x^5 + 20466*x^6 +...
A(x/A(x))^2 = 1 + 2*x + 3*x^2 + 12*x^3 + 87*x^4 + 848*x^5 + 10029*x^6 +...
A(x/A(x)) = 1 + x + x^2 + 5*x^3 + 38*x^4 + 381*x^5 + 4583*x^6 + 63303*x^7 + 977998*x^8 + 16617314*x^9 + 306942415*x^10 +...

Prog

(PARI) {a(n)=local(A=[1, 1]); for(i=1, n, A=concat(A, 0); (A[#A]=-Vec(subst(Ser(A)^2, x, x/Ser(A))/(1+x))[#A])); A[n+1]}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Sequence in context: A294573 A301741 A140763 * A292632 A095789 A134980

Adjacent sequences: A245304 A245305 A245306 * A245308 A245309 A245310

Keyword

nonn

Author

Paul D. Hanna, Jul 21 2014

Status

approved