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A070967
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Sum(binomial(6*n,6*k),k=0..n).
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4
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1, 2, 926, 37130, 2973350, 174174002, 11582386286, 729520967450, 47006639297270, 2999857885752002, 192222214478506046, 12295976362284182570, 787111112023373201990, 50370558298891875954002
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| Matthijs Coster, Supercongruences, Thesis, Jun 08, 1988.
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FORMULA
| G.f.: (1-36x-841x^2+288x^3)/((1-x)(1+27x)(1-64x)). a(n) = ((-27)^n + 1)/3 + (64^n +0^n)/6.
Let b(n)=a(n)-2^(6n)/6 then b(n)+26*b(n-1)-27*b(n-2)=0 - Benoit Cloitre (benoit7848c(AT)orange.fr), May 27 2004
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PROG
| (PARI) a(n)=sum(k=0, n, binomial(6*n, 6*k))
(PARI) a(n)=if(n<0, 0, (2*(-27)^n+2+64^n+0^n)/6)
(PARI) a(n)=if(n<0, 0, polsym(x*(x-64)*(x+27)^2*(x-1)^2, n)[n+1]/6)
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CROSSREFS
| Sequence in context: A159705 A203609 A159723 * A070927 A070922 A176940
Adjacent sequences: A070964 A070965 A070966 * A070968 A070969 A070970
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KEYWORD
| easy,nonn
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AUTHOR
| Sebastian Gutierrez and Sarah Kolitz (skolitz(AT)mit.edu), May 16 2002
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