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 A193545 E.g.f.: 2*L^2/(Pi^2*(1 + 2*Sum_{n>=1} cosh(2*Pi*n*x/L)/cosh(n*Pi) )^2) where L = Lemniscate constant. 5
 1, 0, -2, 0, 0, 0, 144, 0, 0, 0, -96768, 0, 0, 0, 268240896, 0, 0, 0, -2111592333312, 0, 0, 0, 37975288540299264, 0, 0, 0, -1353569484565546795008, 0, 0, 0, 86498911610371173437669376, 0, 0, 0, -9198407234012051081051108278272, 0, 0, 0, 1536583522302562247445395779495133184 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS L = Lemniscate constant = 2*(Pi/2)^(3/2)/gamma(3/4)^2 = 2.62205755429... Compare the definition with that of the dual sequence A193542. LINKS Eric Weisstein's World of Mathematics, Ramanujan Cos/Cosh Identity. FORMULA a(n) = -A193542(n) for n>=1. EXAMPLE E.g.f.: A(x) = 1 - 2*x^2/2! + 144*x^6/6! - 96768*x^10/10! + 268240896*x^14/14! +...+ a(n)*x^n/n! +... which equals the square of the e.g.f. B(x) of A193544: B(x) = 1 - x^2/2! - 3*x^4/4! + 27*x^6/6! + 441*x^8/8! - 11529*x^10/10! - 442827*x^12/12! +... PROG (PARI) {a(n)=local(R, L=2*(Pi/2)^(3/2)/gamma(3/4)^2); R=(sqrt(2)*L/Pi)/(1 + 2*suminf(m=1, cosh(2*Pi*m*x/L +x*O(x^n))/cosh(m*Pi))); round(n!*polcoeff(R^2, n))} CROSSREFS Cf. A193540, A193541, A193542, A193543, A193544. Sequence in context: A218881 A169772 A193542 * A336399 A086260 A124505 Adjacent sequences: A193542 A193543 A193544 * A193546 A193547 A193548 KEYWORD sign AUTHOR Paul D. Hanna, Jul 29 2011 STATUS approved

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Last modified March 24 20:36 EDT 2023. Contains 361510 sequences. (Running on oeis4.)