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 A145228 Scalar product of Atkin polynomial A_n(j) with itself. 0
 1, 393120, 69837768000, 12823035496951680, 2373736216018210243200, 440845278818001523478812800, 82005900318446998074736259577600, 15268862972256859647625489731573696000, 2844591309372269068312979404560741985117440, 530152412660802854746312319621380805036392771200 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..9. M. Kaneko and D. Zagier, Supersingular j-invariants, hypergeometric series and Atkin's orthogonal polynomials, pp. 97-126 of D. A. Buell and J. T. Teitelbaum, eds., Computational Perspectives on Number Theory, Amer. Math. Soc., 1998 FORMULA For formula see Maple code. From Vaclav Kotesovec, Apr 07 2018: (Start) For n > 0, a(n) = 2^(8*n) * 3^(6*n) * (12*n - 7) * Gamma(2*n - 7/6) * Gamma(2*n + 7/6) / (Pi * Gamma(2*n) * Gamma(2*n + 1)). a(n) ~ 2^(8*n + 1) * 3^(6*n + 1) / Pi. (End) MAPLE af:=proc(a, n) mul(a+i, i=0..n-1); end; Aip:=n->(-12)^(6*n+1)*af(-1/12, n)*af(5/12, n)*af(7/12, n)*af(13/12, n)/((2*n-1)!*(2*n)!); MATHEMATICA Flatten[{1, Table[FullSimplify[2^(8*n) * 3^(6*n) * (12*n - 7) * Gamma[2*n - 7/6] * Gamma[2*n + 7/6] / (Pi * Gamma[2*n] * Gamma[2*n + 1])], {n, 1, 15}]}] (* Vaclav Kotesovec, Apr 07 2018 *) CROSSREFS Sequence in context: A345638 A346351 A157623 * A204628 A171439 A210162 Adjacent sequences: A145225 A145226 A145227 * A145229 A145230 A145231 KEYWORD nonn AUTHOR N. J. A. Sloane, Feb 28 2009 STATUS approved

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Last modified March 1 22:23 EST 2024. Contains 370443 sequences. (Running on oeis4.)