A145228 Scalar product of Atkin polynomial A_n(j) with itself.

1, 393120, 69837768000, 12823035496951680, 2373736216018210243200, 440845278818001523478812800, 82005900318446998074736259577600, 15268862972256859647625489731573696000, 2844591309372269068312979404560741985117440, 530152412660802854746312319621380805036392771200

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