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 A275286 a(n) = ((2n+1)!!)^2 * Sum_{k=0..n}(-1)^k/(2k+1)^2. 2
 1, 8, 209, 10016, 822321, 98607816, 16772776929, 3755613340800, 1089481085841825, 392115220017568200, 173351482189397931825, 91513890536903699104800, 57296185618906061753900625, 41706416795344237885218165000, 35120660862575611007699136530625 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Daniel Suteu, Table of n, a(n) for n = 0..99 FORMULA a(0) = 1, a(n) = (2n+1)^2 * a(n-1) + (-1)^n / 4^n * ((2n+1)!)^2 / (n!)^2 / (2n+1)^2. - Daniel Suteu, Jul 21 2016 a(n) ~ A006752 * ((2*n+1)!!)^2. - Daniel Suteu, Dec 03 2016 MATHEMATICA Table[((2 n + 1)!!)^2 Sum[(-1)^k/(2 k + 1)^2, {k, 0, n}], {n, 0, 14}] (* Michael De Vlieger, Jul 21 2016 *) PROG (Sidef) var k = 0 func a(n) { (-1)**n } func b(n) { (2*n + 1)**2 } func g((k)) { b(k) } func g(n) is cached { b(n) * g(n-1) } func f((k)) { a(k) } func f(n) is cached { b(n)*f(n-1) + a(n)*g(n-1) } for i in (k .. 20) { say f(i) } (PARI) dfo(n) = (2*n)! / n! / 2^n; \\ after A001147 a(n) = dfo(n+1)^2*sum(k=0, n, (-1)^k/(2*k+1)^2); \\ Michel Marcus, Jul 25 2016 (Magma) [(Factorial(2*n+1)/(2^n*Factorial(n)))^2*(&+[(-1)^k/(2*k+1)^2: k in [0..n]]): n in [0..20]]; // G. C. Greubel, Aug 25 2018 CROSSREFS Sequence in context: A330287 A279663 A294970 * A255854 A151797 A279464 Adjacent sequences: A275283 A275284 A275285 * A275287 A275288 A275289 KEYWORD easy,nonn AUTHOR Daniel Suteu, Jul 21 2016 STATUS approved

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Last modified September 8 19:44 EDT 2024. Contains 375755 sequences. (Running on oeis4.)