A145493 Coefficients of certain power series associated with Atkin polynomials (see Kaneko-Zagier reference for precise definition).

1, 944, 1054170, 1297994880, 1700941165560, 2326960109485440, 3285120488273369460, 4750462777483659350400, 7000542310802147888540760, 10475220761578770433945887360, 15873347459609903883739895346480, 24308956895577230857746294480107520, 37564030601621705287879755722478648000

Offset: 0

Author

N. J. A. Sloane, Feb 28 2009

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..309
• 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

Crossrefs

Cf. A001421, A145492, A145494.

Programs

PARI

{a(n) = (41*n+77)/2310*(6*n+6)!/((3*n+3)!*n!*(n+2)!^2)} \\ Seiichi Manyama, Aug 19 2018

Formula

a(n) = (A145492(n+1) - A001421(n+1))/330. - Seiichi Manyama, Aug 18 2018

a(n) = ((41*n+77)/2310) * (6*n+6)!/((3*n+3)!*n!*((n+2)!)^2). - Seiichi Manyama, Aug 19 2018

Extensions

More terms from Seiichi Manyama, Aug 18 2018