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 A271843 G.f. A(x) satisfies: A(x) = x + A( x*A(x) + x*A(x)^3 ). 1
 1, 1, 1, 3, 8, 20, 55, 159, 464, 1383, 4200, 12910, 40112, 125832, 397888, 1266848, 4058263, 13070453, 42297553, 137467673, 448499679, 1468388784, 4822816903, 15886282268, 52468807845, 173718343364, 576466929104, 1916968549390, 6387086400663, 21319636605919, 71284279000874, 238724756808108, 800659887614429, 2689098091847122 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Compare g.f. to: C(x) = x + C( x*C(x) + x*C(x)^2 ) where C(x) = x + C(x)^2 is a g.f. of the Catalan numbers (A000108). LINKS Paul D. Hanna, Table of n, a(n) for n = 1..300 FORMULA a(n) ~ c * d^n / n^(3/2), where d = 3.51361449558530219727... and c = 0.1466906366440109... . - Vaclav Kotesovec, Apr 16 2016 EXAMPLE G.f.: A(x) = x + x^2 + x^3 + 3*x^4 + 8*x^5 + 20*x^6 + 55*x^7 + 159*x^8 + 464*x^9 + 1383*x^10 + 4200*x^11 + 12910*x^12 +... where A(x) = x + A( x*A(x) + x*A(x)^3 ). RELATED SERIES. A(x) + A(x)^3 = x + x^2 + 2*x^3 + 6*x^4 + 14*x^5 + 36*x^6 + 103*x^7 + 297*x^8 + 867*x^9 + 2598*x^10 + 7908*x^11 + 24337*x^12 + 75725*x^13 + 237822*x^14 +... PROG (PARI) {a(n) = my(A=x+x^2 +x*O(x^n)); for(i=1, n, A = x + subst(A, x, x*A + x*A^3) ) ; polcoeff(A, n)} for(n=1, 40, print1(a(n), ", ")) CROSSREFS Sequence in context: A230953 A026995 A018035 * A122228 A018790 A268042 Adjacent sequences: A271840 A271841 A271842 * A271844 A271845 A271846 KEYWORD nonn AUTHOR Paul D. Hanna, Apr 15 2016 STATUS approved

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Last modified February 22 16:01 EST 2024. Contains 370256 sequences. (Running on oeis4.)