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 A111994 Sixth convolution of Schroeder's (second problem) numbers A001003(n), n>=0. 1
 1, 6, 33, 176, 930, 4908, 25954, 137712, 733539, 3922834, 21060099, 113481504, 613619332, 3328768344, 18112655748, 98833261600, 540705999621, 2965360687518, 16299708148901, 89784615643728, 495545294427558 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 FORMULA G.f.: ((1+x-sqrt(1-6*x+x^2))/(4*x))^6. a(n)= (6/n)*Sum_{k=1,..,n} binomial(n,k)*binomial(n+k+5,k-1). a(n) = 6*hypergeom([1-n, n+7], [2], -1), n>=1, a(0)=1. Recurrence: n*(n+6)*a(n) = (7*n^2+30*n+5)*a(n-1) - (7*n^2+12*n-22)*a(n-2) + (n-3)*(n+3)*a(n-3). - Vaclav Kotesovec, Oct 18 2012 a(n) ~ 3*sqrt(3*sqrt(2)-4)*(58-41*sqrt(2)) * (3+2*sqrt(2))^(n+6)/(16*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 18 2012 MATHEMATICA CoefficientList[Series[((1+x-Sqrt[1-6*x+x^2])/(4*x))^6, {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 18 2012 *) PROG (PARI) x='x+O('x^50); Vec(((1+x-sqrt(1-6*x+x^2))/(4*x))^6) \\ G. C. Greubel, Mar 16 2017 CROSSREFS Cf. Sixth column of convolution triangle A011117. Sequence in context: A106850 A284076 A094165 * A092851 A137627 A138395 Adjacent sequences: A111991 A111992 A111993 * A111995 A111996 A111997 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Sep 12 2005 STATUS approved

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Last modified August 15 11:07 EDT 2024. Contains 375173 sequences. (Running on oeis4.)