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A224873
Triangle of coefficients T(n, k) (n > 0, k < n) in expansion of sin(u*x) * sin(v*x) / (cos(u*x) + cos(v*x)), read by rows.
0
1, 1, 1, 3, 25, 3, 17, 329, 329, 17, 155, 5325, 14301, 5325, 155, 2073, 110605, 563013, 563013, 110605, 2073, 38227, 2918825, 23904881, 45956625, 23904881, 2918825, 38227, 929569, 96075665, 1150348017, 3600524785, 3600524785, 1150348017, 96075665, 929569
OFFSET
1,4
FORMULA
A024235(n) = Sum_{k = 0..n-1} T(n, k).
A110501(n) = T(n, 0).
E.g.f.: sin(u*x) * sin(v*x) / (cos(u*x) + cos(v*x)) = Sum_{n>0, k<n} x^(2*n) / (2*n)! * u^(2*k + 1) * v^(2*n - 2*k -1) * T(n, k).
EXAMPLE
1; 1, 1; 3, 25, 3; 17, 329, 329, 17; ...
PROG
(PARI) {T(n, k) = local(u = 'u, v = 'v, A); if( n<0 || k>=n, 0, n = 2*n; k = 2*k + 1; A = x * O(x^n); n! * polcoeff( polcoeff( polcoeff( sin( u*x + A) * sin( v*x + A) / (cos( u*x + A) + cos( v*x + A)), n, x), k, u), n - k, v))}
CROSSREFS
Sequence in context: A080202 A300945 A234319 * A085836 A073916 A076962
KEYWORD
nonn,tabl
AUTHOR
Michael Somos, Jul 23 2013
STATUS
approved