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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
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
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.)