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Search: id:A136526
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| A136526 |
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Coefficients of a special solution of a hypergeometric-type polynomial recursion: B(x, n) = ((1 + a + b)*x - c)*B(x, n - 1) - a*b*B(x, n - 2); a=3,b=2,c=0;. |
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+0
1
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| 1, 0, 1, -6, 0, 6, 0, -42, 0, 36, 36, 0, -288, 0, 216, 0, 468, 0, -1944, 0, 1296, -216, 0, 4536, 0, -12960, 0, 7776, 0, -4104, 0, 38880, 0, -85536, 0, 46656, 1296, 0, -51840, 0, 311040, 0, -559872, 0, 279936, 0, 32400, 0, -544320, 0, 2379456, 0, -3639168, 0, 1679616, -7776, 0, 505440, 0, -5132160, 0, 17635968, 0
(list; table; graph; listen)
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OFFSET
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1,4
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COMMENT
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Row sums are:
{1, 1, 0, -6, -36, -180, -864, -4104, -19440, -92016, -435456}
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REFERENCES
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Harry Hochstadt, The Functions of Mathematical Physics, Dover, New York, 1986, page 93
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FORMULA
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a=3,b=2,c=0; B(x, 0) = 1; B(x, 1) = x; B(x, n) = ((1 + a + b)*x - c)*B(x, n - 1) - a*b*B(x, n - 2);
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EXAMPLE
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{1},
{0, 1},
{-6, 0, 6},
{0, -42, 0, 36},
{36, 0, -288, 0,216},
{0, 468, 0, -1944, 0, 1296},
{-216,0, 4536, 0, -12960, 0, 7776},
{0, -4104, 0, 38880, 0, -85536, 0, 46656},
{1296, 0, -51840, 0, 311040, 0, -559872, 0, 279936},
{0, 32400, 0, -544320, 0, 2379456, 0, -3639168, 0, 1679616},
{-7776, 0, 505440, 0, -5132160, 0, 17635968, 0, -23514624, 0, 10077696}
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MATHEMATICA
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Clear[B, x, n, f, a, b, c] a = (b + 1)/(b - 1); c = 0; b = 2; B[x, 0] = 1; B[x, 1] = x; B[x_, n_] := B[x, n] = ((1 + a + b)*x - c)*B[x, n - 1] - a*b*B[x, n - 2]; a0 = Table[CoefficientList[B[x, n], x], {n, 0, 10}]; Flatten[a0]
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CROSSREFS
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Sequence in context: A010677 A021169 A064373 this_sequence A097715 A092605 A004016
Adjacent sequences: A136523 A136524 A136525 this_sequence A136527 A136528 A136529
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KEYWORD
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nonn,uned,tabl
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AUTHOR
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Roger L. Bagula, Mar 23 2008
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