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A136526 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;. 0
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; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Row sums are:

{1, 1, 0, -6, -36, -180, -864, -4104, -19440, -92016, -435456}

REFERENCES

Harry Hochstadt, The Functions of Mathematical Physics, Dover, New York, 1986, page 93

LINKS

Table of n, a(n) for n=1..63.

FORMULA

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);

EXAMPLE

{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}

MATHEMATICA

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]

CROSSREFS

Sequence in context: A195290 A280692 A161419 * A097715 A316710 A198499

Adjacent sequences:  A136523 A136524 A136525 * A136527 A136528 A136529

KEYWORD

uned,tabl,sign

AUTHOR

Roger L. Bagula, Mar 23 2008

STATUS

approved

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Last modified October 18 10:05 EDT 2019. Contains 328146 sequences. (Running on oeis4.)