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 A098400 a(n) = 4^n*binomial(2*n+1, n). 6
 1, 12, 160, 2240, 32256, 473088, 7028736, 105431040, 1593180160, 24216338432, 369849532416, 5671026163712, 87246556364800, 1346089726771200, 20819521107394560, 322702577164615680, 5011381198321090560, 77954818640550297600, 1214454016715941478400 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS G. C. Greubel, Table of n, a(n) for n = 0..820 FORMULA G.f.: (1-sqrt(1-16*x))/(8*x*sqrt(1-16*x)). E.g.f.: a(n) = n! * [x^n] exp(8*x)*(BesselI(0, 8*x) + BesselI(1, 8*x)). - Peter Luschny, Aug 25 2012 (n+1)*a(n) - 8*(2*n+1)*a(n-1) = 0. - R. J. Mathar, Nov 26 2012 a(n) = 4^n*(2*n+1)*Hypergeometric2F1([1-n,-n],[2],1). - Peter Luschny, Sep 22 2014 From G. C. Greubel, Dec 27 2023: (Start) a(n) = 4^n * A001700(n). a(n) = 4^n * (2*n+1) * A000108(n). a(n) = (2*n+1) * A151403(n). (End) From Amiram Eldar, Jan 16 2024: (Start) Sum_{n>=0} 1/a(n) = 8/15 + 128*arcsin(1/4)/(15*sqrt(15)). Sum_{n>=0} (-1)^n/a(n) = 8/17 + 128*arcsinh(1/4)/(17*sqrt(17)). (End) MATHEMATICA Table[4^n Binomial[2n+1, n], {n, 0, 20}] (* Harvey P. Dale, Jan 22 2019 *) PROG (PARI) a(n)=binomial(2*n+1, n)<<(2*n) \\ Charles R Greathouse IV, Oct 23 2023 (Magma) [4^n*(2*n+1)*Catalan(n): n in [0..30]]; // G. C. Greubel, Dec 27 2023 (SageMath) [4^n*binomial(2*n+1, n) for n in range(31)] # G. C. Greubel, Dec 27 2023 CROSSREFS Cf. A000108, A001700, A069720, A069723, A098399, A151403. Sequence in context: A091019 A355844 A219418 * A208791 A019578 A144346 Adjacent sequences: A098397 A098398 A098399 * A098401 A098402 A098403 KEYWORD easy,nonn AUTHOR Paul Barry, Sep 06 2004 STATUS approved

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Last modified August 5 17:25 EDT 2024. Contains 374953 sequences. (Running on oeis4.)