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 A167893 a(n) = Sum_{k=1..n} Catalan(k)^3. 3
 1, 9, 134, 2878, 76966, 2376934, 81330523, 3005537523, 117938569451, 4856184495787, 208008478587443, 9208478072445171, 419215292661445171, 19548493234125829171, 930767164551264230296, 45133682592532326893296, 2224173698690413601132296, 111192059034974606204132296 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Catalan(k) = A000108(k) = (2k)!/k!/(k+1)! = C(2*k,k)/(k+1). For prime p=7 p^2 divides a(p^2) and p divides all a(n) for n from (p^2-1)/2 to p^2-2. For prime p=19 or 97, p divides all a(n) for n from (p-1)/2 to p-2. LINKS G. C. Greubel, Table of n, a(n) for n = 1..500 Eric Weisstein's World of Mathematics, Catalan Number FORMULA a(n) = Sum_{k=1..n} A033536(k). Recurrence: (n+1)^3*a(n) = (5*n - 1)*(13*n^2 - 16*n + 7)*a(n-1) - 8*(2*n - 1)^3*a(n-2). - Vaclav Kotesovec, Jul 01 2016 a(n) ~ 2^(6*n+6) / (63*Pi^(3/2)*n^(9/2)). - Vaclav Kotesovec, Jul 01 2016 MATHEMATICA Array[n \[Function] Sum[CatalanNumber[k]^3, {k, 1, n}], 15] (* J. Mulder, (jasper.mulder(AT)planet.nl), Jan 25 2010 *) Accumulate[CatalanNumber[Range[1, 20]]^3] (* Vincenzo Librandi, Jul 01 2016 *) PROG (PARI) a(n)=sum(k=1, n, (binomial(k+k, k)/(k+1))^3) /* Charles R Greathouse IV, Jun 14 2011 */ (MAGMA) [&+[Catalan(i)^3: i in [1..n]]: n in [1..20]]; // Vincenzo Librandi, Jul 01 2016 CROSSREFS Cf. A000108, A014138, A167892, A167893, A001246, A033536, A014137, A094639. Sequence in context: A163200 A279975 A296171 * A268062 A218326 A272498 Adjacent sequences:  A167890 A167891 A167892 * A167894 A167895 A167896 KEYWORD nonn AUTHOR Alexander Adamchuk, Nov 15 2009 EXTENSIONS More terms from J. Mulder, (jasper.mulder(AT)planet.nl), Jan 25 2010 More terms from Sean A. Irvine, Jun 13 2011 STATUS approved

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Last modified December 12 18:43 EST 2018. Contains 318081 sequences. (Running on oeis4.)