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A053134
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Binomial coefficients C(2n+4,4).
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6
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1, 15, 70, 210, 495, 1001, 1820, 3060, 4845, 7315, 10626, 14950, 20475, 27405, 35960, 46376, 58905, 73815, 91390, 111930, 135751, 163185, 194580, 230300, 270725, 316251, 367290, 424270, 487635, 557845, 635376, 720720, 814385, 916895, 1028790, 1150626, 1282975
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Even indexed members of fifth column of Pascal's triangle A007318.
Number of standard tableaux of shape (2n+1,1^4). - Emeric Deutsch, May 30 2004
Number of integer solutions to -n <= x <= y <= z <= w <= n. - Michael Somos, Dec 28 2011
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..200
Milan Janjic, Two Enumerative Functions
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FORMULA
| a(n) = binomial(2*n+4, 4) = A000332(2*n+4).
G.f.: (1+10*x+5*x^2)/(1-x)^5.
a(1 - n) = A053126(n). - Michael Somos, Dec 28 2011
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EXAMPLE
| 1 + 15*x + 70*x^2 + 210*x^3 + 495*x^4 + 1001*x^5 + 1820*x^6 + 3060*x^7 + ...
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PROG
| (MAGMA) [Binomial(2*n+4, 4): n in [0..30]]; // Vincenzo Librandi, Oct 07 2011
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CROSSREFS
| Cf. A000447, A002299, A053126, A000332.
Sequence in context: A085474 A124893 A126402 * A000475 A145053 A168298
Adjacent sequences: A053131 A053132 A053133 * A053135 A053136 A053137
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KEYWORD
| nonn,easy
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)
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