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 A118969 a(n) = 2*binomial(5*n+1,n)/(4*n+2). 8
 1, 2, 11, 80, 665, 5980, 56637, 556512, 5620485, 57985070, 608462470, 6474009360, 69682358811, 757366074080, 8300675584120, 91634565938880, 1018002755977245, 11372548404732930, 127677890035721025, 1439777493407492640 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS A quadrisection of A118968. If y = x + 2*x^3 + x^5, the series reversion is x = y - 2*y^3 + 11*y^5 - 80*y^7 + 665*y^9 - ... - R. J. Mathar, Sep 29 2012 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..100 Karol A. Penson and Karol Zyczkowski, Product of Ginibre matrices: Fuss-Catalan and Raney distribution, arXiv:1103.3453 [math-ph], 2011. Karol A. Penson and Karol Zyczkowski, Product of Ginibre matrices: Fuss-Catalan and Raney distribution, Phys. Rev. E 83, 061118 (2011). FORMULA From Gary W. Adamson, Aug 11 2011: (Start) a(n) is sum of top row terms in M^n, where M is an infinite square production matrix with the tetrahedral series in each column (A000292), as follows:    1,  1,  0,  0,  0,  0, ...    4,  1,  1,  0,  0,  0, ...   10, 10,  4,  1,  0,  0, ...   20, 20, 10,  4,  1,  0, ...   35, 35, 20, 10,  4,  1, ...   ... (End) G.f.: hypergeom([1/5, 2/5, 3/5, 4/5],[1/2, 3/4, 5/4], 3125*x/256)^2. - Mark van Hoeij, Apr 19 2013 a(n) = 2*binomial(5n+1,n-1)/n for n>0, a(0)=1. - Bruno Berselli, Jan 19 2014 8*n*(4*n+1)*(2*n+1)*(4*n-1)*a(n) - 5*(5*n+1)*(5*n-3)*(5*n-2)*(5*n-1)*a(n-1) = 0. - R. J. Mathar, Oct 10 2014 EXAMPLE a(3) = 80 = sum of top row terms in M^n = (35 + 35 + 9 + 1). MATHEMATICA Table[2*Binomial[5n+1, n]/(4n+2), {n, 0, 20}] (* Harvey P. Dale, Aug 21 2011 *) PROG (MAGMA) [2*Binomial(5*n+1, n)/(4*n+2): n in [0..20]]; // Vincenzo Librandi, Aug 12 2011 (PARI) a(n)=2*binomial(5*n+1, n)/(4*n+2); \\ Joerg Arndt, Apr 20 2013 CROSSREFS Cf. A000292, A118968. Sequence in context: A099661 A027110 A341955 * A181068 A056846 A277500 Adjacent sequences:  A118966 A118967 A118968 * A118970 A118971 A118972 KEYWORD nonn,easy AUTHOR Paul Barry, May 07 2006 STATUS approved

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Last modified September 17 03:42 EDT 2021. Contains 347478 sequences. (Running on oeis4.)