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Search: id:A082649
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| A082649 |
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Triangle of coefficients in expansion of sin^2 (nx) in powers of sin x. |
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+0
1
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| 1, 4, 4, 16, 24, 9, 64, 128, 80, 16, 256, 640, 560, 200, 25, 1024, 3072, 3456, 1792, 420, 36, 4096, 14336, 19712, 13440, 4704, 784, 49
(list; table; graph; listen)
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OFFSET
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1,2
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REFERENCES
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Herb Conn, HCR 83, Box 93, Custer, SD 57730
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FORMULA
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If we change all (-) coefficient signs, to (+), then coefficients are: are 4^(n-1), (2n)4^(n-2), (2n)(2n-3)4^(n-3)/2!, (2n)(2n-4)(2n-5)4^(n-4)/3!, (2n)(2n-5)(2n-6)(2n-7)4^(n-5)/4!, (2n)(2n-6)(2n-7)(2n-8)(2n-9)4^(n-6)/5!...
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EXAMPLE
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sin^2 x = sin^2 x
sin^2 2x = -4sin^4 x + 4sin^2 x
sin^2 3x = 16 sin^6 x - 24 sin^4 x + 9 sin^2 x
sin^2 4x = -64 sin^8 x + 128 sin^6 x - 80 sin^4 x + 16 sin^2 x
sin^2 5x = 256 sin^10 x - 640 sin^8 x + 560 sin^6 x - 200 sin^4 x + 25 sin^2 x
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CROSSREFS
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A001108 gives row sums.
Adjacent sequences: A082646 A082647 A082648 this_sequence A082650 A082651 A082652
Sequence in context: A141125 A129884 A137725 this_sequence A053441 A065732 A092959
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KEYWORD
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nonn,tabl
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), May 16 2003
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