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A141947
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A manufactured symmetrical triangular sequence of coefficients based on: t(n,m)=(Gamma[1 - m + n] Hypergeometric2F1Regularized[1, 1 + 2 m - n, 2 + m, -1])/Gamma[ -2 m + n]. The function is taken have backward and half forward.
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0
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0, 0, 1, 1, 0, 3, 3, 0, 1, 7, 7, 1, 0, 4, 15, 15, 4, 0, 1, 11, 31, 31, 11, 1, 0, 5, 26, 63, 63, 26, 5, 0, 1, 16, 57, 127, 127, 57, 16, 1, 0, 6, 42, 120, 255, 255, 120, 42, 6, 0, 1, 22, 99, 247, 511, 511, 247, 99, 22, 1, 0, 7, 64, 219, 502, 1023, 1023, 502, 219, 64, 7, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,6
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COMMENTS
| Row sums are:
{0, 2, 6, 16, 38, 86, 188, 402, 846, 1760, 3630}.
The odd n row are the most interesting.
The function was abstracted from the Mathematica generating function for
A052509 by taking out the powers of two:
t(n,m)=(n - m)!*(2^(-m + n)/Gamma[1 - m + n] - Hypergeometric2F1[1, 1 + 2 m - n, 2 + m, -1]/(Gamma[2 + m] Gamma[ -2 m + n])).
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FORMULA
| t(n,m)=(Gamma[1 - m + n] Hypergeometric2F1Regularized[1, 1 + 2 m - n, 2 + m, -1])/Gamma[ -2 m + n].
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EXAMPLE
| {0, 0},
{1, 1},
{0, 3, 3, 0},
{1, 7, 7, 1},
{0, 4, 15, 15, 4, 0},
{1, 11, 31, 31, 11, 1},
{0, 5, 26, 63, 63, 26, 5, 0},
{1, 16, 57, 127, 127, 57, 16, 1},
{0, 6, 42, 120, 255, 255, 120, 42, 6, 0},
{1, 22, 99, 247, 511, 511, 247, 99, 22, 1},
{0, 7, 64, 219, 502, 1023, 1023, 502, 219, 64, 7, 0}
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MATHEMATICA
| In[97]:= Table[Join[Table[(Gamma[1-m+n] Hypergeometric2F1Regularized[1, 1+2 m-n, 2+m, -1])/Gamma[ -2 m+n], {m, Floor[n/2], 0, -1}], Table[(Gamma[1-m+n] Hypergeometric2F1Regularized[1, 1+2 m-n, 2+m, -1])/Gamma[ -2 m+n], {m, 0, Floor[n/2]}]], {n, 0, 10}]; Flatten[%]
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CROSSREFS
| Cf. A052509.
Sequence in context: A102752 A104548 A085707 * A010607 A118522 A098316
Adjacent sequences: A141944 A141945 A141946 * A141948 A141949 A141950
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KEYWORD
| nonn,uned
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AUTHOR
| Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Sep 14 2008
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