A273172 - OEIS

%I #10 Jun 23 2016 06:56:49

%S 1,4,12,8,48,80,64,64,320,448,128,64,320,1792,2304,512,512,1024,7168,

%T 9216,11264,1024,4096,4096,14336,6144,45056,53248,16384,49152,81920,

%U 16384,147456,180224,212992,245760,32768,24576,40960,16384,147456,90112,106496,983040,1114112,131072,131072,327680,65536,65536,720896,3407872,1310720,4456448,4980736,262144,1572864,524288,917504,393216,11534336,13631488,1572864,8912896,19922944,22020096

%N Triangle for denominators of coefficients for integrated odd powers of cos(x) in terms sin((2*m+1)*x).

%C For the numerator triangle see A273171, also for the cos^(2*n+1) formula, and the Gradstein-Ryshik reference.

%F a(n, m) = denominator(R(n, m)) with the rationals R(n, m) = (1/2^(2*n))* binomial(2*n+1, n-m) / (2*m+1) for m = 0, ..., n, n >= 0. See the Gradstein-Ryshik reference given in A273171 (where the sin arguments are falling).

%e The triangle a(n, m) begins:

%e n\m    0    1    2     3    4     5     6 ...

%e 0:     1

%e 1:     4   12

%e 2:     8   48   80

%e 3:    64   64  320   448

%e 4:   128   64  320  1792 2304

%e 5:   512  512 1024  7168 9216 11264

%e 6:  1024 4096 4096 14336 6144 45056 53248

%e ...

%e row 7: 16384 49152 81920 16384 147456 180224 212992 245760,

%e row 8: 32768 24576 40960 16384 147456 90112 106496 983040 1114112,

%e row 9: 131072 131072 327680 65536 65536 720896 3407872 1310720 4456448 4980736,

%e row 10: 262144 1572864 524288 917504 393216 11534336 13631488 1572864 8912896 19922944 22020096,...

%e For the head of the rational triangle see A273171.

%o (PARI) a(n, m) = denominator((1/2^(2*n))*binomial(2*n+1, n-m)/(2*m+1));

%o tabl(nn) = for (n=0, nn, for (k=0, n, print1(a(n,k), ", ")); print()); \\ _Michel Marcus_, Jun 19 2016

%Y Cf. A273171.

%K nonn,tabl,frac,easy

%O 0,2

%A _Wolfdieter Lang_, Jun 13 2016