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 A191417 G.f. C(x) satisfies: C(C(x)) - S(S(x)) = x where C(x) = x + 2*x^2*S(x). 4
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified April 20 17:12 EDT 2024. Contains 371845 sequences. (Running on oeis4.)