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 A143475 Numerator of the coefficient of z^(2n) in the Stirling-like asymptotic expansion of the hyperfactorial function A002109. 10
 1, 1, -1433, 1550887, -365236274341, 31170363588856607, -2626723351027654662151, 127061942835077684151157039, -5696145248370283185291966600124423, 254326794362835881966596504823903633657, -33203124408022060010631772664020406983485604379 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 REFERENCES Mohammad K. Azarian, On the Hyperfactorial Function, Hypertriangular Function, and the Discriminants of Certain Polynomials, International Journal of Pure and Applied Mathematics, Vol. 36, No. 2, 2007, pp. 251-257. Mathematical Reviews, MR2312537. Zentralblatt MATH, Zbl 1133.11012. LINKS Seiichi Manyama, Table of n, a(n) for n = 0..113 Eric Weisstein's World of Mathematics, Hyperfactorial FORMULA From Seiichi Manyama, Aug 31 2018: (Start) Let B_n be the Bernoulli number, and define the sequence {c_n} by the recurrence c_0 = 1, c_n = (-1/(2*n)) * Sum_{k=0..n-1} B_{2*n-2*k+2}*c_k/((2*n-2*k+1)*(2*n-2*k+2)) for n > 0. a(n) is the numerator of c_n. (End) EXAMPLE (Glaisher*(1 - 1433/(7257600*z^4) + 1/(720*z^2))*z^(1/12 + (z*(1 + z))/2))/e^(z^2/4). From Seiichi Manyama, Aug 31 2018: (Start) c_1 = -1/2 * (B_4*c_0/(3*4)) = 1/720, so a(1) = 1. c_2 = -1/4 * (B_6*c_0/(5*6) + B_4*c_1/(3*4)) = -1433/7257600, so a(2) = -1433. (End) CROSSREFS Cf. A002109, A143476. Sequence in context: A205070 A169822 A114083 * A245948 A221004 A204862 Adjacent sequences:  A143472 A143473 A143474 * A143476 A143477 A143478 KEYWORD sign,frac AUTHOR Eric W. Weisstein, Aug 19 2008 EXTENSIONS More terms from Seiichi Manyama, Aug 31 2018 STATUS approved

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Last modified April 18 15:51 EDT 2021. Contains 343089 sequences. (Running on oeis4.)