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A137668 Triangle read by rows: coefficients from the expansion of p(x,t) = tan(x*arctan(t)) which is in the Chebyshevlike form: T(t,x) = cos(x*arccos(t)). 0
0, 1, 0, -2, 0, 2, 0, 24, 0, -40, 0, 16, 0, -720, 0, 1568, 0, -1120, 0, 272, 0, 40320, 0, -104704, 0, 102144, 0, -45696, 0, 7936, 0, -3628800, 0, 10720512, 0, -12869120, 0, 8042496, 0, -2618880, 0, 353792, 0, 479001600, 0, -1565051904, 0, 2188865536, 0, -1712668672, 0, 789854208, 0, -202369024, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Row sums are {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...}.

The polynomials are not orthogonal on a Chebyshev weighted domain.

REFERENCES

Chang and Sederberg, Over and Over Again, MAA, 1997, page 111.

LINKS

Table of n, a(n) for n=1..55.

FORMULA

T(n,m) = n! * coefficients(p(x,n)), odd-indexed terms only, where p(x,t) = tan(x*arctan(t)) = Sum_{n>=0} P(x,n)*t^n/n!.

EXAMPLE

{0, 1},

{0, -2, 0, 2},

{0, 24, 0, -40, 0, 16},

{0, -720, 0, 1568, 0, -1120, 0, 272},

{0, 40320, 0, -104704, 0, 102144, 0, -45696, 0, 7936},

{0, -3628800, 0, 10720512, 0, -12869120, 0, 8042496, 0, -2618880, 0, 353792}, {0, 479001600, 0, -1565051904, 0, 2188865536, 0, -1712668672, 0, 789854208, 0, -202369024, 0, 22368256},

{0, -87178291200,0, 309188763648, 0, -487356047360, 0, 450481647616,0, -263012372480, 0, 96327655424, 0, -20355112960, 0, 1903757312},

{0, 20922789888000, 0, -79493016453120, 0, 138125290635264, 0, -145543597588480, 0, 101310804328448, 0, -47338162094080, 0, 14395135885312, 0, -2589109944320, 0, 209865342976},

{0, -6402373705728000, 0, 25804966598737920, 0,-48657759347146752, 0, 57064887390568448, 0, -45634645720694784, 0, 25589689363070976, 0, -9984529525374976, 0, 2597395096141824, 0, -406719034687488, 0, 29088885112832}

MATHEMATICA

p[t_] = Tan[x*ArcTan[t]];

g = Table[ ExpandAll[n!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]], {n, 1, 20, 2}];

a = Table[ CoefficientList[n!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n], x], {n, 1, 20, 2}];

Flatten[a]

CROSSREFS

Sequence in context: A057498 A137949 A019214 * A056615 A060989 A135298

Adjacent sequences:  A137665 A137666 A137667 * A137669 A137670 A137671

KEYWORD

tabf,sign

AUTHOR

Roger L. Bagula, Apr 27 2008

STATUS

approved

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Last modified November 25 19:33 EST 2020. Contains 338625 sequences. (Running on oeis4.)