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Search: id:A047835
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| A047835 |
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a(n)=Product_{i=1..n} ((i+4)*(i+5)*(i+6)*(i+7))/(i*(i+1)*(i+2)*(i+3)). |
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4
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| 1, 70, 1764, 24696, 232848, 1646568, 9343620, 44537922, 184225041, 677352676, 2254684432, 6892441920, 19571505408, 52101067968, 131018862096, 313203587004, 715536058545, 1569305708586, 3316911815140, 6778924352200, 13435361082000
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Number of tilings of a <4,n,4> hexagon.
Partial sums of A133708. - Peter Bala (pbala(AT)toucansurf.com), Sep 21 2007
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REFERENCES
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O. D. Anderson, Find the next sequence, J. Rec. Math., 8 (No. 4, 1975-1976), 241.
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FORMULA
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a(n)=C(n,n-1)*C(n+1,n-2)*C(n+2,n-3)*C(n+3,n-4)/(10*4!), n>=4 . - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 29 2007
a(n-4) = 1/3456*sum {1 <= x_1, x_2, x_3, x_4 <= n} (det V(x_1,x_2,x_3,x_4))^2 = 1/3456*sum {1 <= i,j,k,l <= n} ((i-j)(i-k)(i-l)(j-k)(j-l)(k-l))^2, where V(x_1,x_2,x_3,x_4) is the Vandermonde matrix of order 4. - Peter Bala (pbala(AT)toucansurf.com), Sep 21 2007
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MAPLE
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seq(binomial(n, n-1)*binomial(n+1, n-2)*binomial(n+2, n-3)*binomial(n+3, n-4)/(10*4!), n=4..24); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 29 2007
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CROSSREFS
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Fourth row of array A103905.
Cf. A002415, A047819, A133708.
Sequence in context: A107421 A076430 A006296 this_sequence A133312 A093757 A006437
Adjacent sequences: A047832 A047833 A047834 this_sequence A047836 A047837 A047838
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KEYWORD
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nonn
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AUTHOR
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njas
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