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 A144617 Triangle read by rows: numerators of coefficients of the Debye-type polynomial u_n used for asymptotic Airy-type expansions of Bessel functions of arbitrary large order. 3
 1, 3, -5, 81, -462, 385, 30375, -369603, 765765, -425425, 4465125, -94121676, 349922430, -446185740, 185910725, 1519035525, -49286948607, 284499769554, -614135872350, 566098157625, -188699385875 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Chris Kormanyos, Rows n=0..121 of triangle, flattened M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972. See Section 9.3.9. M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy]. See Section 9.3.9. EXAMPLE The polynomials u_0, u_1, u_2 and u_3 are: 1 (3 t - 5 t^3)/24 (81 t^2 - 462 t^4 + 385 t^6)/1152 (30375 t^3 - 369603 t^5 + 765765 t^7 - 425425 t^9)/414720 MATHEMATICA uktop = {1, 3, -5}; ukbot = {1, 24}; u = ((3 t) - (5 (t^3)))/24; Do[uk = (((1/2) (t^2) (1 - (t^2))) D[u, t]) + ((1/8) Integrate[((1 - (5 (t^2))) u), {t, 0, t}]); u = Simplify[uk]; Do[uktop = Append[uktop, Coefficient[Expand[Numerator[u]], t^n]], {n, k, 3 k, 2}]; ukbot = Append[ukbot, Denominator[u]]; Print[k], {k, 2, 8}]; [From Chris Kormanyos (ckormanyos(AT)yahoo.com), Jan 18 2009] CROSSREFS For denominators see A144618. Cf. A144622. Sequence in context: A145616 A122912 A062214 * A107655 A182234 A082715 Adjacent sequences:  A144614 A144615 A144616 * A144618 A144619 A144620 KEYWORD sign,frac,tabl AUTHOR N. J. A. Sloane, Jan 15 2009, based on email from Chris Kormanyos (ckormanyos(AT)yahoo.com) EXTENSIONS Added terms up to u_5 Chris Kormanyos (ckormanyos(AT)yahoo.com), Jan 18 2009 STATUS approved

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