A191419 G.f. C(C(x)) where C(x) is the g.f. of A191417.

1, 0, 0, 8, 0, 0, 128, 0, 0, 2560, 0, 0, 60416, 0, 0, 1728512, 0, 0, 63438848, 0, 0, 3096477696, 0, 0, 196811685888, 0, 0, 15408280109056, 0, 0, 1413600665141248, 0, 0, 147160243434946560, 0, 0, 17047411713181220864, 0, 0, 2169625122325921792000

Offset

1,4

Comments

Functions C(x) and S(x) satisfy: C(C(x)) - S(S(x)) = x and C(x) = x + 2*x^2*S(x), where C(x) is the g.f. of A191417 and S(x) is the g.f. of A191418.

Links

Table of n, a(n) for n=1..40.

Example

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

Crossrefs

Cf. A191417 (C(x)), A191418 (S(x)).

Sequence in context: A371665 A169696 A192059 * A054373 A061847 A307224

Adjacent sequences: A191416 A191417 A191418 * A191420 A191421 A191422

Keyword

nonn

Author

Paul D. Hanna, Jun 01 2011

Status

approved