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A051836
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n*(n+1)*(n+2)*(n+3)*(3*n+2)/120.
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5
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0, 1, 8, 33, 98, 238, 504, 966, 1716, 2871, 4576, 7007, 10374, 14924, 20944, 28764, 38760, 51357, 67032, 86317, 109802, 138138, 172040, 212290, 259740, 315315, 380016, 454923, 541198, 640088, 752928, 881144, 1026256, 1189881, 1373736
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| 5-dimensional version of pentagonal-based pyramidal numbers. - Ben Creech (mathroxmysox(AT)yahoo.com)
If Y is a 3-subset of an n-set X then, for n>=7, a(n-6) is the number of 7-subsets of X having at least two elements in common with Y. - Milan R. Janjic (agnus(AT)blic.net), Nov 23 2007
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REFERENCES
| A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
Herbert John Ryser, Combinatorial Mathematics, "The Carus Mathematical Monographs", No. 14, John Wiley and Sons, 1963, pps. 1-8.
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FORMULA
| a(n)=C(n+4, n)*(3n+5)/5
G.f.: (1+2*x)/(1-x)^6.
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MAPLE
| with (combinat):a[0]:=0:for n from 1 to 50 do a[n]:=stirling2(n+2, n)+a[n-1] od: seq(a[n], n=0..34); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 17 2008
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MATHEMATICA
| Table[n(n + 1)(n + 2)(n + 3)(3n + 2)/120, {n, 0, 60}] (* From Vladimir Joseph Stephan Orlovsky, Apr 08 2011 *)
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CROSSREFS
| Partial sums of A001296.
Cf. A093560 ((3, 1) Pascal, column m=5).
Sequence in context: A114105 A014820 A070736 * A070051 A087235 A048877
Adjacent sequences: A051833 A051834 A051835 * A051837 A051838 A051839
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KEYWORD
| easy,nonn
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AUTHOR
| Barry E. Williams, Dec 12 1999
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EXTENSIONS
| More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Nov 18 2004
Simpler definition from Ben Creech (mathroxmysox(AT)yahoo.com), Nov 13 2005
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