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A112415
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a(n) = C(1+n,1) * C(2+n,1) * C(4+n,2).
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2
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12, 60, 180, 420, 840, 1512, 2520, 3960, 5940, 8580, 12012, 16380, 21840, 28560, 36720, 46512, 58140, 71820, 87780, 106260, 127512, 151800, 179400, 210600, 245700, 285012, 328860, 377580, 431520
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OFFSET
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0,1
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..680
Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1).
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FORMULA
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From R. J. Mathar, Aug 15 2008: (Start)
a(n) = (n+1)*(n+2)*(n+3)*(n+4)/2 = A033486(n+1) = 12*A000332(n+4).
O.g.f.: 12/(1-x)^5. (End)
From a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5); a(0)=12, a(1)=60, a(2)=180, a(3)=420, a(4)=840. - Harvey P. Dale, Jul 24 2011
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EXAMPLE
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n=0: C(1+0,1)*C(2+0,1)*C(4+0,2) = C(1,1)*C(2,1)*C(4,2) = 1*2*6 = 12;
n=10: C(1+10,1)*C(2+10,1)*C(4+10,2) = C(11,1)*C(12,1)*C(14,2) = 11*12*91 = 12012.
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MATHEMATICA
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Table[(n+1)(n+2)Binomial[4+n, 2], {n, 0, 30}] (* or *) LinearRecurrence[ {5, -10, 10, -5, 1}, {12, 60, 180, 420, 840}, 31] (* Harvey P. Dale, Jul 24 2011 *)
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PROG
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(MAGMA) [(n+1)*(n+2)*(n+3)*(n+4)/2: n in [0..40]]; // Vincenzo Librandi, Apr 28 2011
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CROSSREFS
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Sequence in context: A000141 A279509 A008530 * A033486 A174642 A061624
Adjacent sequences: A112412 A112413 A112414 * A112416 A112417 A112418
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KEYWORD
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easy,nonn
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AUTHOR
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Zerinvary Lajos, Dec 09 2005
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STATUS
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approved
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