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A050486
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C(n+6,6)*(2n+7)/7.
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11
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1, 9, 44, 156, 450, 1122, 2508, 5148, 9867, 17875, 30888, 51272, 82212, 127908, 193800, 286824, 415701, 591261, 826804, 1138500, 1545830, 2072070, 2744820, 3596580, 4665375, 5995431, 7637904, 9651664, 12104136, 15072200, 18643152
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| If a 2-set Y and an (n-3)-set Z are disjoint subsets of an n-set X then a(n-8) is the number of 8-subsets of X intersecting both Y and Z. - Milan R. Janjic (agnus(AT)blic.net), Sep 08 2007
7-dimensional square numbers, sixth partial sums of binomial transform of [1,2,0,0,0,...]. a(n)=sum{i=0,n,C(n+6,i+6)*b(i)}, where b(i)=[1,2,0,0,0,...]. [From Borislav St. Borisov (b.st.borisov(AT)abv.bg), Mar 05 2009]
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REFERENCES
| A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
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LINKS
| Milan Janjic, Two Enumerative Functions
Matthew M. Conroy, Home page (listed instead of email address)
Index entries for sequences related to Chebyshev polynomials.
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FORMULA
| a(n)= ((-1)^n)*A053120(2*n+7, 7)/64 (1/64 of eighth unsigned column of Chebyshev T-triangle, zeros omitted).
G.f.: (1+x)/(1-x)^8.
a(n)=2*C(n+7, 7)-C(n+6, 6). - Paul Barry (pbarry(AT)wit.ie), Mar 04 2003
a(n)=C(n+6,6)+2*C(n+6,7) [From Borislav St. Borisov (b.st.borisov(AT)abv.bg), Mar 05 2009]
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MATHEMATICA
| s1=s2=s3=s4=s5=0; lst={}; Do[s1+=n^2; s2+=s1; s3+=s2; s4+=s3; s5+=s4; AppendTo[lst, s5], {n, 0, 7!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 15 2009]
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CROSSREFS
| Partial sums of A040977.
Cf. A005585, A040977 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 15 2009]
Sequence in context: A161457 A162212 A161733 * A036599 A059825 A074631
Adjacent sequences: A050483 A050484 A050485 * A050487 A050488 A050489
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KEYWORD
| easy,nonn
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AUTHOR
| Barry E. Williams, Dec 26 1999
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EXTENSIONS
| More terms from Matthew M. Conroy, May 23 2001
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