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A192071 G.f. C(x) satisfies: C(C(x)) + S(S(x)) = x such that C(x)^3 + (3/2)*S(x)^3 = x^3. 2
1, 0, 0, -108, 0, 0, -46656, 0, 0, -56267136, 0, 0, -91334158848, 0, 0, -187875634540032, 0, 0, -452928490364583936, 0, 0, -1241099993772119162880, 0, 0, -3783238246806589528473600, 0, 0, -12650825837219458785210335232, 0, 0, -45942311360783796910833996398592, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Table of n, a(n) for n=1..33.

FORMULA

Functions C(x) and S(x) satisfy:

(1) C'(C(x)) *C'(x) + S'(S(x)) *S'(x) = 1,

(2) C(x)^2 *C'(x) + (3/2)*S(x)^2 *S'(x) = x^2.

EXAMPLE

G.f.: C(x) = x - 108*x^4 - 46656*x^7 - 56267136*x^10 - 91334158848*x^13 - 187875634540032*x^16 -...

Related expansions:

S(x) = 6*x^2 + 648*x^5 + 793152*x^8 + 1262231424*x^11 + 2646377775360*x^14 + 6519085424584704*x^17 +...

C(C(x)) = x - 216*x^4 - 46656*x^7 - 64665216*x^10 - 99769190400*x^13 - 209379250944000*x^16 -...

S(S(x)) = 216*x^4 + 46656*x^7 + 64665216*x^10 + 99769190400*x^13 + 209379250944000*x^16 +...

C(x)^3 = x^3 - 324*x^6 - 104976*x^9 - 139828032*x^12 - 232643612160*x^15 - 491365348803072*x^18 -...

S(x)^3 = 216*x^6 + 69984*x^9 + 93218688*x^12 + 155095741440*x^15 + 327576899202048*x^18 +...

PROG

(PARI) {a(n)=local(C=x, S=6*x^2, Cv=[1, 0, 0, -108]);

for(i=0, n\3, Cv=concat(Cv, [0, 0, 0]); C=x*Ser(Cv); S=((x^3-C^3)*2/3)^(1/3);

Cv[#Cv]=-polcoeff((subst(C, x, C)+subst(S, x, S))*3/2, #Cv); ); polcoeff(C, n)}

CROSSREFS

Cf. A192072 (S(x)), A192073 (C(C(x))); variants: A192057, A191417.

Sequence in context: A145045 A113471 A057388 * A025601 A109005 A036196

Adjacent sequences:  A192068 A192069 A192070 * A192072 A192073 A192074

KEYWORD

sign

AUTHOR

Paul D. Hanna, Jun 22 2011

STATUS

approved

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Last modified June 18 11:14 EDT 2018. Contains 305554 sequences. (Running on oeis4.)