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A133766
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a(n) = (4*n+1)*(4*n+3)*(4*n+5).
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4
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15, 315, 1287, 3315, 6783, 12075, 19575, 29667, 42735, 59163, 79335, 103635, 132447, 166155, 205143, 249795, 300495, 357627, 421575, 492723, 571455, 658155, 753207, 856995, 969903, 1092315, 1224615, 1367187, 1520415, 1684683, 1860375
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OFFSET
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0,1
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REFERENCES
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Jolley, Summation of Series, Dover (1961).
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LINKS
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Table of n, a(n) for n=0..30.
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
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FORMULA
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G.f.: 3*(5 + 85*x + 39*x^2 - x^3)/(1-x)^4 .
E.g.f: (15 + 300*x + 336*x^2 + 64*x^3)*exp(x) .
sum(4/((4*m+1)*(4*m+3)*(4*m+5)), m=0..infinity) = (Pi-2)/4. [Jolley eq 238]
a(0)=15, a(1)=315, a(2)=1287, a(3)=3315; for n>3, a(n) = 4*a(n-1)-6*a(n-2)+ 4*a(n-3)- a(n-4). - Harvey P. Dale, May 06 2012
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MAPLE
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seq((4*n+1)*(4*n+3)*(4*n+5), n=0..40);
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MATHEMATICA
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Table[c=4n; (c+1)(c+3)(c+5), {n, 0, 30}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {15, 315, 1287, 3315}, 30] (* Harvey P. Dale, May 06 2012 *)
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PROG
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(PARI) a(n)=(4*n+1)*(4*n+3)*(4*n+5) \\ Charles R Greathouse IV, Oct 16 2015
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CROSSREFS
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Sequence in context: A105491 A158533 A284070 * A289951 A112489 A062757
Adjacent sequences: A133763 A133764 A133765 * A133767 A133768 A133769
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KEYWORD
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nonn,easy
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AUTHOR
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Miklos Kristof, Jan 02 2008
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STATUS
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approved
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