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A191419 G.f. C(C(x)) where C(x) is the g.f. of A191417. 4
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 (list; graph; refs; listen; history; text; internal format)
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: A126270 A169696 A192059 * A054373 A061847 A164790

Adjacent sequences:  A191416 A191417 A191418 * A191420 A191421 A191422

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jun 01 2011

STATUS

approved

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Last modified December 11 11:31 EST 2017. Contains 295876 sequences.