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A112851
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a(n) = (n-1)*n*(n+1)*(n+2)*(2*n+1)/40.
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3
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0, 0, 3, 21, 81, 231, 546, 1134, 2142, 3762, 6237, 9867, 15015, 22113, 31668, 44268, 60588, 81396, 107559, 140049, 179949, 228459, 286902, 356730, 439530, 537030, 651105, 783783, 937251, 1113861, 1316136, 1546776, 1808664, 2104872, 2438667, 2813517, 3233097
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| A112851 is the fourth sequence in A112852.
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FORMULA
| 4*a(n+1) = 1*2^2*3 + 2*3^2+4 + 3*4^2*5 + .. (n terms). [Jolley, Summation of Series (1961), eq (54) page 10]
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MAPLE
| a:=n->sum(j^4-j^2, j=0..n)/4: seq(a(n), n=0..36); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 08 2008
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MATHEMATICA
| a[n_]:=(n-1)n(n+1)(n+2)(2n+1)/40; Table[a[n], {n, 30}] (Locker)
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CROSSREFS
| Partial sums of sequence A006011.
Cf. A112852.
Sequence in context: A067002 A110450 A102832 * A034490 A071351 A083231
Adjacent sequences: A112848 A112849 A112850 * A112852 A112853 A112854
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KEYWORD
| easy,nonn
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AUTHOR
| Alford Arnold (Alford1940(AT)aol.com), Sep 24 2005
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EXTENSIONS
| More terms from Josh Locker (jlocker(AT)mail.rochester.edu) and Michael W. Motily (mwm5036(AT)psu.edu), Oct 04 2005
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