A191417 G.f. C(x) satisfies: C(C(x)) - S(S(x)) = x where C(x) = x + 2*x^2*S(x).

1, 0, 0, 4, 0, 0, 32, 0, 0, 384, 0, 0, 6912, 0, 0, 202752, 0, 0, 9060352, 0, 0, 537133056, 0, 0, 38729089024, 0, 0, 3250319523840, 0, 0, 309812206239744, 0, 0, 33002445042876416, 0, 0, 3882425071117008896, 0, 0, 499695395684082515968, 0, 0

Offset

1,4

Comments

S(x) is the g.f. of A191418, and C(C(x)) is the g.f. of A191419.

Links

Table of n, a(n) for n=1..42.

Formula

Functions C(x) and S(x) satisfy: C'(C(x))*C'(x) - S'(S(x))*S'(x) = 1.

Example

G.f. C(x) = x + 4*x^4 + 32*x^7 + 384*x^10 + 6912*x^13 + 202752*x^16 +...
Related expansions.
S(x) = 2*x^2 + 16*x^5 + 192*x^8 + 3456*x^11 + 101376*x^14 +...
C(C(x)) = x + 8*x^4 + 128*x^7 + 2560*x^10 + 60416*x^13 + 1728512*x^16 +...
S(S(x)) = 8*x^4 + 128*x^7 + 2560*x^10 + 60416*x^13 + 1728512*x^16 +...

Prog

(PARI) {a(n)=local(C=x, S=2*x^2, Sv=[0, 2]);
for(i=0, n\3, Sv=concat(Sv, [0, 0, 0]); S=x*Ser(Sv); C=x+2*x^2*S;
Sv[#Sv]=polcoeff((subst(C, x, C)-subst(S, x, S))/4, #Sv+2); ); polcoeff(C, n)}

Crossrefs

Cf. A191418 (S(x)), A191419 (C(C(x))).

Sequence in context: A307186 A060784 A181204 * A307050 A223179 A278272

Adjacent sequences: A191414 A191415 A191416 * A191418 A191419 A191420

Keyword

nonn

Author

Paul D. Hanna, Jun 01 2011

Status

approved