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Search: id:A079727
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| A079727 |
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a(n)=1+C(2,1)^3+C(4,2)^3+...+C(2n,n)^3. |
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+0
9
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| 1, 9, 225, 8225, 351225, 16354233, 805243257, 41229480825, 2172976383825, 117106008311825, 6423711336265041, 357470875526646609, 20131502573232075025, 1145190201805448075025, 65706503254247744075025
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n) seems to have an interesting congruence property: For p prime, a(p)==8 (mod p) if and only p == 3, 5, 7, or 13 (mod 14); i.e. iff p=7 or p is in A003625.
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FORMULA
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a(n)=sum(k=0, n, binomial(2*k, k)^3)
G.f.: hypergeom([1/2, 1/2, 1/2], [1, 1], 64*x)/(1-x). - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 18 2003
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PROGRAM
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(PARI) a(n)=sum(k=0, n, binomial(2*k, k)^3)
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CROSSREFS
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Cf. A002476, A006134 (sum(k=0, n, binomial(2*k, k)).
Sequence in context: A063392 A012831 A012749 this_sequence A128492 A001818 A095363
Adjacent sequences: A079724 A079725 A079726 this_sequence A079728 A079729 A079730
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 17 2003
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