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 A272461 G.f. A(x) satisfies: A( x - A(x^4)/x^2 ) = x. 2
 1, 1, 2, 5, 14, 43, 140, 474, 1650, 5865, 21194, 77623, 287492, 1074915, 4051824, 15381073, 58749102, 225621404, 870686810, 3374625925, 13130575110, 51271434788, 200845390668, 789081913225, 3108496250028, 12275905239752, 48590260462470, 192736593501813, 766007363990640, 3049978926971396, 12164745517874576, 48596364360237882, 194426663474794450, 778968350863994065 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Paul D. Hanna, Table of n, a(n) for n = 1..300 FORMULA a(n) ~ c * d^n / n^(3/2), where d = 4.1920029654932692520828... and c = 0.1046247209912855075794... . - Vaclav Kotesovec, May 03 2016 EXAMPLE G.f.: A(x) = x + x^2 + 2*x^3 + 5*x^4 + 14*x^5 + 43*x^6 + 140*x^7 + 474*x^8 + 1650*x^9 + 5865*x^10 + 21194*x^11 + 77623*x^12 +... where A( x - A(x^4)/x^2 ) = x. RELATED SERIES. Let B(x) be the series reversion of the g.f. A(x) so that A(B(x)) = x, then B(x) = x - x^2 - x^6 - 2*x^10 - 5*x^14 - 14*x^18 - 43*x^22 - 140*x^26 - 474*x^30 - 1650*x^34 - 5865*x^38 - 21194*x^42 - 77623*x^46 +... such that B(x) = x - A(x^4)/x^2. PROG (PARI) {a(n) = my(A=x); for(i=1, n, A = serreverse( x - subst(A, x, x^4 +x^3*O(x^n))/x^2 )); polcoeff(A, n)} for(n=1, 50, print1(a(n), ", ")) CROSSREFS Cf. A141200, A272460. Sequence in context: A066351 A181496 A276989 * A213264 A029889 A307787 Adjacent sequences: A272458 A272459 A272460 * A272462 A272463 A272464 KEYWORD nonn AUTHOR Paul D. Hanna, Apr 29 2016 STATUS approved

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Last modified August 12 02:57 EDT 2024. Contains 375085 sequences. (Running on oeis4.)