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A132117
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Binomial transform of [1, 7, 17, 17, 6, 0, 0, 0, ...].
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6
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1, 8, 32, 90, 205, 406, 728, 1212, 1905, 2860, 4136, 5798, 7917, 10570, 13840, 17816, 22593, 28272, 34960, 42770, 51821, 62238, 74152, 87700, 103025, 120276, 139608, 161182, 185165, 211730, 241056, 273328, 308737, 347480, 389760, 435786, 485773, 539942, 598520
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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Let M = the infinite lower triangular matrix of the natural numbers: [1; 2,3; 4,5,6; ...]; and V = [1, 2, 3, ...]. Then M*V = A132117.
a(n) = (4*n + 6*n^2 + 8*n^3 + 6*n^4)/24. - Alois P. Heinz, Aug 07 2008
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EXAMPLE
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a(3) = 32 = (1, 2, 1) dot (1, 7, 17) = (1 + 14 + 17).
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MAPLE
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a:= n-> (Matrix([[0, 0, 2, 13, 46]]). Matrix(5, (i, j)-> if (i=j-1) then 1 elif j=1 then [5, -10, 10, -5, 1][i] else 0 fi)^n)[1, 1]: seq(a(n), n=1..29); # Alois P. Heinz, Aug 07 2008
a:= n-> (4+(6+(8+6*n)*n)*n)*n/24: seq(a(n), n=1..40); # Alois P. Heinz, Aug 07 2008
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MATHEMATICA
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Table[(4 n + 6 n^2 + 8 n^3 + 6 n^4) / 24, {n, 50}] (* Vincenzo Librandi, Jun 21 2013 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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