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A101097
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n*(n+1)*(n+2)*(n+3)*(n+4)*(2+4*n+n^2)/840.
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8
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1, 12, 69, 272, 846, 2232, 5214, 11088, 21879, 40612, 71643, 121056, 197132, 310896, 476748, 713184, 1043613, 1497276, 2110273, 2926704, 3999930, 5393960, 7184970, 9462960, 12333555, 15919956, 20365047, 25833664, 32515032, 40625376, 50410712
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Fourth partial sums of cubes (A000578).
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LINKS
| C. Rossiter, Depictions, Explorations and Formulas of the Euler/Pascal Cube.
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FORMULA
| This sequence could be obtained from the general formula a(n)=n*(n+1)*(n+2)*(n+3)* ...* (n+k) *(n*(n+k) + (k-1)*k/6)/((k+3)!/6) at k=4 - Alexander R. Povolotsky (pevnev(AT)juno.com), May 17 2008
O.g.f.: x(1+4x+x^2)/(1-x)^8. - R. J. Mathar, Jun 13 2008
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MATHEMATICA
| s1=s2=s3=s4=0; lst={}; Do[s1+=n^3; s2+=s1; s3+=s2; s4+=s3; AppendTo[lst, s4], {n, 0, 6!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 15 2009]
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PROG
| (PARI) {A101097(n) =
n*(n+1)*(n+2)*(n+3)*(n+4)*(2+4*n+n^2)/840
} /* R. J. Mathar, Dec 06 2011 */
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CROSSREFS
| Cf. A101102, A101094, A024166, A000537.
Sequence in context: A059585 A050484 A096425 * A067702 A163193 A088832
Adjacent sequences: A101094 A101095 A101096 * A101098 A101099 A101100
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KEYWORD
| easy,nonn
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AUTHOR
| Cecilia Rossiter (cecilia(AT)noticingnumbers.net), Dec 15 2004
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EXTENSIONS
| Edited by Ralf Stephan, Dec 16 2004
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