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A093567
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Binomial (Binomial (n,2), 3) - Binomial (Binomial (n,3), 2).
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0
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0, 1, 14, 75, 265, 735, 1736, 3654, 7050, 12705, 21670, 35321, 55419, 84175, 124320, 179180, 252756, 349809, 475950, 637735, 842765, 1099791, 1418824, 1811250, 2289950, 2869425, 3565926, 4397589, 5384575, 6549215, 7916160, 9512536
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,3
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COMMENTS
| All terms are positive: A093566 >= A054563 ==> C( C(n,2), 3) >= C( C(n,3), 2) ==> n^2*(n^4 + 3n^3 -35n^2 + 69n -38)/144 >= 0 ==> (n - 2)(n - 1)(n^2 + 6n - 19) ==> 0 which it is for all n >= 2.
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REFERENCES
| Solomon W. Golomb, Iterated binomial coefficients, Amer. Math. Monthly, 87 (1980), 719-727.
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
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FORMULA
| a(n) = A093566(n) - A054563(n).
G.f.: x^3*(-1-7*x+2*x^2+x^3)/(x-1)^7. [R. J. Mathar, Dec 08 2010]
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MATHEMATICA
| Table[ Binomial[ Binomial[n, 2], 3] - Binomial[ Binomial[n, 3], 2], {n, 2, 34}]
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CROSSREFS
| Sequence in context: A167633 A196411 A108650 * A200554 A152100 A173962
Adjacent sequences: A093564 A093565 A093566 * A093568 A093569 A093570
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KEYWORD
| nonn
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AUTHOR
| Robert G. Wilson v (rgwv(AT)rgwv.com) and Santino Spadaro (spadaro(AT)nabanassar.com), Mar 31 2004
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