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 A009564 E.g.f. sin(x^2)/2, coefficients of x^(4*n + 2). 4
 1, -60, 15120, -8648640, 8821612800, -14079294028800, 32382376266240000, -101421602465863680000, 415017197290314178560000, -2149789081963827444940800000, 13750050968240640337841356800000, -106425394494182556214892101632000000, 980390734080409707851586040233984000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS G. C. Greubel, Table of n, a(n) for n = 0..182 FORMULA a(n) = (-1)^n*(2+4*n)!/(2*(1+2*n)!) = (-1)^n*A001813(2*n+1)/2. - Robert Israel, Dec 21 2015 MAPLE seq(i!*coeff(series(sin(x^2)/2, x, 4*i+4), x, i), i=2..54, 4); # Peter Luschny, Dec 14 2012 MATHEMATICA nmax = 12; coes = CoefficientList[ Series[ Sin[x^2]/2, {x, 0, 4*nmax + 2}], x]; a[n_] := coes[[4*n + 3]]*(4*n + 2)!; Table[a[n], {n, 0, nmax}] (* Jean-François Alcover, Dec 14 2012 *) Table[(-1)^n (2 + 4 n)!/(2 (1 + 2 n)!), {n, 0, 25}] (* Vincenzo Librandi, Dec 22 2015 *) PROG (Sage) def A009564(n):     return falling_factorial(4*n+2, 2*n+1)/(2*(-1)^n) [A009564(n) for n in (0..12)]  # Peter Luschny, Dec 14 2012 (MAGMA) [(-1)^n*Factorial(2+4*n)/(2*Factorial(1+2*n)): n in [0..20]]; // Vincenzo Librandi, Dec 22 2015 (PARI) a(n) = (-1)^n*(2+4*n)!/(2*(1+2*n)!); \\ Altug Alkan, Dec 22 2015 CROSSREFS Cf. A001813, A103639, A024343, A075069. Sequence in context: A184890 A295598 A113424 * A269762 A291912 A001460 Adjacent sequences:  A009561 A009562 A009563 * A009565 A009566 A009567 KEYWORD sign AUTHOR EXTENSIONS Extended with signs Mar 1997 Definition corrected and terms a(10)-a(12) from Peter Luschny, Dec 14 2012 STATUS approved

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Last modified February 28 00:28 EST 2020. Contains 332319 sequences. (Running on oeis4.)