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 A143927 G.f. satisfies: A(x) = (1 + x*A(x) + x^2*A(x)^2)^2. 13
 1, 2, 7, 28, 123, 572, 2769, 13806, 70414, 365636, 1926505, 10273870, 55349155, 300783420, 1646828655, 9075674700, 50304255210, 280248358964, 1568399676946, 8813424968192, 49709017472751, 281306750922072, 1596802663432503 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Vladimir Kruchinin and D. V. Kruchinin, Composita and their properties, arXiv:1103.2582 [math.CO], 2011-2013. FORMULA Self-convolution of A006605. Bisection of A143926. a(n) = ((24*n+12)*A006605(n) + (3*n+5)*A006605(n+1))/(13*n+17). - Mark van Hoeij, Jul 14 2010 a(n) = (1/(n+1))*Sum_{j=0..2*n+2} (binomial(j,2*j-3*n-4)*binomial(2*n+2 ,j)). - Vladimir Kruchinin, Dec 24 2010 a(n) = GegenbauerPoly(n,-2n-2,-1/2)/(n+1). - Emanuele Munarini, Oct 20 2016 a(n) = T(2*n+2, n)/(n+1), where T(n,k) = A027907(n,k). - Emanuele Munarini, Oct 20 2016 The g.f. A(x) satisfies 1 + x*A'(x)/A(x) = 1 + 2*x + 10*x^2 + 50*x^3 + 266*x^3 + ..., the g.f. of A027908. - Peter Bala, Aug 03 2023 MATHEMATICA Table[GegenbauerC[n, -2n-2, -1/2]/(n+1), {n, 0, 12}] (* Emanuele Munarini, Oct 20 2016 *) n = 20; A = Sum[a[k] x^k, {k, 0, n}] + x O[x]^n; Table[a[k], {k, 0, n}] /. Reverse[Solve[LogicalExpand[(1 + x A + x^2 A^2)^2 == A]]] (* Emanuele Munarini, Oct 20 2016 *) PROG (PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=(1+x*A+x^2*A^2)^2); polcoeff(A, n)} (Maxima) makelist(ultraspherical(n, -2*n-2, -1/2)/(n+1), n, 0, 12); /* Emanuele Munarini, Oct 20 2016 */ CROSSREFS Cf. A006605, A027908, A143926. Sequence in context: A005435 A291091 A215973 * A253787 A060379 A002931 Adjacent sequences: A143924 A143925 A143926 * A143928 A143929 A143930 KEYWORD nonn AUTHOR Paul D. Hanna, Sep 08 2008 STATUS approved

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Last modified August 11 13:56 EDT 2024. Contains 375069 sequences. (Running on oeis4.)