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A101094
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n*(n+1)*(n+2)*(n+3)*(1+3*n+n^2)/120.
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7
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1, 11, 57, 203, 574, 1386, 2982, 5874, 10791, 18733, 31031, 49413, 76076, 113764, 165852, 236436, 330429, 453663, 612997, 816431, 1073226, 1394030, 1791010, 2277990, 2870595, 3586401, 4445091, 5468617, 6681368, 8110344, 9785336
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Partial sums of A024166. Third partial sums of cubes (A000578).
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LINKS
| C. Rossiter, Depictions, Explorations and Formulas of the Euler/Pascal Cube.
Index to sequences with linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
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FORMULA
| This sequence could be obtained from the general formula n*(n+1)*(n+2)*(n+3)* ...* (n+k) *(n*(n+k) + (k-1)*k/6)/((k+3)!/6) at k=3. - Alexander R. Povolotsky (pevnev(AT)juno.com), May 17 2008
G.f. -x*(1+4*x+x^2) / (x-1)^7 . - R. J. Mathar, Dec 06 2011
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MATHEMATICA
| s1=s2=s3=0; lst={}; Do[s1+=n^3; s2+=s1; s3+=s2; AppendTo[lst, s3], {n, 0, 6!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 15 2009]
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PROG
| (PARI) a(n)=sum(l=1, n, sum(j=1, l, sum(m=1, j, sum(i=m*(m+1)/2-m+1, m*(m+1)/2, (2*i-1))))) - Alexander R. Povolotsky (pevnev(AT)juno.com), May 17 2008
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CROSSREFS
| Cf. A101097, A101102, A000537.
Sequence in context: A201150 A114030 A071984 * A187693 A200529 A014470
Adjacent sequences: A101091 A101092 A101093 * A101095 A101096 A101097
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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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