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A014410
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Elements in Pascal's triangle (by row) that are not 1.
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14
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2, 3, 3, 4, 6, 4, 5, 10, 10, 5, 6, 15, 20, 15, 6, 7, 21, 35, 35, 21, 7, 8, 28, 56, 70, 56, 28, 8, 9, 36, 84, 126, 126, 84, 36, 9, 10, 45, 120, 210, 252, 210, 120, 45, 10, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 12, 66, 220, 495, 792, 924, 792, 495, 220, 66, 12, 13, 78
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OFFSET
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2,1
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COMMENTS
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Also, rows of triangle formed using Pascal's rule except begin and end n-th row with n+2 - Asher Auel (asher.auel(AT)reed.edu).
Row sums are A000918. - Roger L. Bagula and Gary W. Adamson, Jan 15 2009
Given the triangle signed by rows (+ - + ...) = M, with V = a variant of the Bernoulli numbers starting [1/2, 1/6, 0, -1/30, 0, 1/42,...]; M*V = [1, 1, 1,...]. - Gary W. Adamson, Mar 05 2012
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LINKS
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_Reinhard Zumkeller_, Rows n=2..150 of triangle, flattened
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FORMULA
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a(n) = C(A003057(n),A002260(n)) = C(A003057(n),A004736(n)). - Lekraj Beedassy, Jul 29 2006
t(n,j) = ( Gamma[4 + n]/(Gamma[2 + j] Gamma[3 - j + n]) - KroneckerDelta[ -4 - n]). [From Roger L. Bagula and Gary W. Adamson, Jan 15 2009]
T(n,k) = A028263(n,k) - A007318(n,k). [Reinhard Zumkeller, Mar 12 2012]
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EXAMPLE
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2
3, 3
4, 6, 4
5, 10, 10, 5
6, 15, 20, 15, 6
7, 21, 35, 35, 21, 7
8, 28, 56, 70, 56, 28, 8
9, 36, 84, 126, 126, 84, 36, 9
10, 45, 120, 210, 252, 210, 120, 45, 10
11, 55, 165, 330, 462, 462, 330, 165, 55, 11
12, 66, 220, 495, 792, 924, 792, 495, 220, 66, 12
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MAPLE
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for i from 0 to 12 do seq(binomial(i, j)*1^(i-j), j = 1 .. i-1) od; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 02 2007
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MATHEMATICA
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Select[ Flatten[ Table[ Binomial[ n, i ], {n, 0, 13}, {i, 0, n} ] ], #>1& ]
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PROG
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(Haskell)
a014410 n k = a014410_tabl !! (n-2) !! (k-2)
a014410_row n = a014410_tabl !! (n-2)
a014410_tabl = map (init . tail) $ drop 2 a007318_tabl
-- Reinhard Zumkeller, Mar 12 2012
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CROSSREFS
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Cf. A007318.
Cf. A000918
Cf. A027641, the Bernoulli numbers
Sequence in context: A203996 A059442 A225273 * A180986 A200763 A203291
Adjacent sequences: A014407 A014408 A014409 * A014411 A014412 A014413
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KEYWORD
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nonn,easy,tabl
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AUTHOR
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Mohammad K. Azarian
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EXTENSIONS
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More terms from Erich Friedman.
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STATUS
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approved
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