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Search: id:A101097
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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; listen)
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OFFSET
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1,2
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LINKS
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C. Rossiter, Depictions, Explorations and Formulas of the Euler/Pascal Cube.
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FORMULA
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a(n) = {(n*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(2 + n*(4 + n)))/840}.
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)^(k+4), k=4. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 13 2008
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PROGRAM
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(PARI) a(n)=sum(s=1, n, sum(l=1, s, 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
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Cf. A101102, A101094.
Cf. A101102, A101094, A024166, A000537.
Sequence in context: A059585 A050484 A096425 this_sequence A067702 A088832 A060930
Adjacent sequences: A101094 A101095 A101096 this_sequence A101098 A101099 A101100
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KEYWORD
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easy,nonn
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AUTHOR
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Cecilia Rossiter (cecilia(AT)noticingnumbers.net), Dec 15 2004
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EXTENSIONS
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Edited by Ralf Stephan, Dec 16 2004
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