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A100381
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2^n*binomial(n,2).
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3
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0, 0, 4, 24, 96, 320, 960, 2688, 7168, 18432, 46080, 112640, 270336, 638976, 1490944, 3440640, 7864320, 17825792, 40108032, 89653248, 199229440, 440401920, 968884224, 2122317824, 4630511616, 10066329600, 21810380800, 47110422528
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| Jolley, Summation of Series, Dover (1961), eq (214) page 40.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..3000
Index to sequences with linear recurrences with constant coefficients, signature (6,-12,8).
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FORMULA
| 1-log(2) = 0.3068528... is the sum of reciprocals of a(n), n=2,3,4,... (log means natural logarithm) - Graeme McRae (g_m(AT)mcraefamily.com), Jul 28 2006
a(n)=sum(k*2^k, k=0..n) = 2*A001815(n). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 09 2006
E.g.f.:2x^2*exp(2x)
a(n) = 4*A001788(n-1). - Johannes W. Meijer (meijgia(AT)hotmail.com), Jun 27 2009
sum_{j=1..k} (j+2)/a(j+1) = 1-1/((k+1)*2^k). [Jolley]
G.f. -4*x^2 / (2*x-1)^3 . - R. J. Mathar, Oct 05 2011
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MAPLE
| seq(2^n*binomial(n, 2), n=0..20);
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MATHEMATICA
| Range[0, 20]! CoefficientList[Series[2x^2 Exp[2x], {x, 0, 20}], x]
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PROG
| (Other) SAGE: [lucas_number2(n, 2, 0)*binomial(n, 2) for n in xrange(0, 20)] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 10 2009]
(MAGMA) [4*n*(n+1)*2^(n-2) : n in [-1..30]]; // Vincenzo Librandi, Oct 06 2011
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CROSSREFS
| Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Jun 27 2009: Appears in A162007.
Sequence in context: A009769 A119878 A054603 * A091143 A119920 A100738
Adjacent sequences: A100378 A100379 A100380 * A100382 A100383 A100384
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KEYWORD
| nonn
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AUTHOR
| Jorge Coveiro (jorgecoveiro(AT)yahoo.com), Dec 30 2004
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