This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A259557 a(n) = binomial(4*n-1, 2*n). 0
 1, 3, 35, 462, 6435, 92378, 1352078, 20058300, 300540195, 4537567650, 68923264410, 1052049481860, 16123801841550, 247959266474052, 3824345300380220, 59132290782430712, 916312070471295267, 14226520737620288370 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Essentially the same as A100033. LINKS V. V. Kruchinin and D. V. Kruchinin, A Generating Function for the Diagonal T_{2n,n} in Triangles, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.6. FORMULA G.f. A(x)=1+x*B(x)'/B(x), where B(x) is g.f. of A079489. a(n) = A100033(n-1) for n>0. n*(2*n-1)*a(n) -2*(4*n-1)*(4*n-3)*a(n-1)=0. - R. J. Mathar, Jul 06 2015 a(n) = [x^(2*n)] 1/(1 - x)^(2*n). - Ilya Gutkovskiy, Oct 10 2017 MATHEMATICA Table[Binomial[4 n - 1, 2 n], {n, 0, 30}] (* Vincenzo Librandi, Jul 01 2015 *) PROG (PARI) vector(20, n, n--; binomial(4*n-1, 2*n)) \\ Michel Marcus, Jul 01 2015 (MAGMA) [Binomial(4*n-1, 2*n): n in [0..20]]; // Vincenzo Librandi, Jul 01 2015 CROSSREFS Cf. A001700, A079489, A100033. Sequence in context: A161495 A179135 A100033 * A184554 A046032 A304191 Adjacent sequences:  A259554 A259555 A259556 * A259558 A259559 A259560 KEYWORD nonn,easy AUTHOR Vladimir Kruchinin, Jun 30 2015 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 17 06:52 EDT 2019. Contains 327119 sequences. (Running on oeis4.)