%I A095704
%S A095704 1,2,0,3,0,1,4,0,4,0,5,0,10,0,1,6,0,20,0,6,0,7,0,35,0,21,0,1,8,0,56,0,
%T A095704 56,0,8,0,9,0,84,0,126,0,36,0,1,10,0,120,0,252,0,120,0,10,0,11,0,165,0,
%U A095704 462,0,330,0,55,0,1,12,0,220,0,792,0,792,0,220,0,12,0,13,0,286,0,1287,
               0
%V A095704 1,2,0,3,0,-1,4,0,-4,0,5,0,-10,0,1,6,0,-20,0,6,0,7,0,-35,0,21,0,-1,8,0,
               -56,0,56,0,-8,0,
%W A095704 9,0,-84,0,126,0,-36,0,1,10,0,-120,0,252,0,-120,0,10,0,11,0,-165,0,462,
               0,-330,0,55,0,
%X A095704 -1,12,0,-220,0,792,0,-792,0,220,0,-12,0,13,0,-286,0,1287,0
%N A095704 Triangle read by rows giving coefficients of the trigonometric expansion 
               of sin(n*x).
%F A095704 T(n,k)=C(n+1,k+1)*sin(pi*(k+1)/2); - Paul Barry (pbarry(AT)wit.ie), May 
               21 2006
%e A095704 The trigonometric expansion of sin(4x) is 4*cos(x)^3*sin(x) - 4*cos(x)*sin(x)^3, 
               so the fourth row is 4, 0, -4, 0.
%e A095704 Triangle begins:
%e A095704 1
%e A095704 2 0
%e A095704 3 0 -1
%e A095704 4 0 -4 0
%e A095704 5 0 -10 0 1
%e A095704 6 0 -20 0 6 0
%e A095704 7 0 -35 0 21 0 -1
%e A095704 8 0 -56 0 56 0 -8 0
%t A095704 Flatten[ Table[ Plus @@ CoefficientList[ TrigExpand[ Sin[n*x]], {Sin[x], 
               Cos[x]}], {n, 13}]]
%Y A095704 First column is A000027 = C(n, 1), third column is A000292 = C(n, 3), 
               fifth column is A000389 = C(n, 5), seventh column is A000580 = C(n, 
               7), ninth column is A000582 = C(n, 9).
%Y A095704 A001288 = C(n, 11), A010966 = C(n, 13), A010968 = C(n, 15), A010970 = 
               C(n, 17), A010972 = C(n, 19),
%Y A095704 A010974 = C(n, 21), A010976 = C(n, 23), A010978 = C(n, 25), A010980 = 
               C(n, 27), A010982 = C(n, 29),
%Y A095704 A010984 = C(n, 31), A010986 = C(n, 33), A010988 = C(n, 35), A010990 = 
               C(n, 37), A010992 = C(n, 39),
%Y A095704 A010994 = C(n, 41), A010996 = C(n, 43), A010998 = C(n, 45), A011090 = 
               C(n, 47), A017713 = C(n, 49)
%Y A095704 Another version of the triangle in A034867. Cf. A096754.
%Y A095704 A017715 = C(n, 51), A017717 = C(n, 53), A017719 = C(n, 55), A017721 = 
               C(n, 57), etc.
%Y A095704 Sequence in context: A088673 A035614 A133735 this_sequence A163496 A092241 
               A128144
%Y A095704 Adjacent sequences: A095701 A095702 A095703 this_sequence A095705 A095706 
               A095707
%K A095704 sign,tabl
%O A095704 1,2
%A A095704 Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 06 2004