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}]; (* Chris Kormanyos (ckormanyos(AT)yahoo.com), Jan 18 2009 *)
CROSSREFS
KEYWORD
AUTHOR
N. J. A. Sloane, Jan 15 2009, based on email from Chris Kormanyos (ckormanyos(AT)yahoo.com)
EXTENSIONS
Terms up to u_5 from Chris Kormanyos (ckormanyos(AT)yahoo.com), Jan 18 2009
STATUS
approved