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A169937
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a(n) = binomial(m+n-1,n)^2 - binomial(m+n,n+1)*binomial(m+n-2,n-1) with m = 14.
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4
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1, 91, 3185, 63700, 866320, 8836464, 71954064, 488259720, 2848181700, 14620666060, 67255063876, 281248448936, 1081724803600, 3863302870000, 12914469594000, 40680579221100, 121443493851225, 345280521733875, 938920716995625, 2451077240157000, 6162708489537600
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OFFSET
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0,2
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COMMENTS
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REFERENCES
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S. Mukai, An Introduction to Invariants and Moduli, Cambridge, 2003; Prop. 8.4, case n=14.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (25, -300, 2300, -12650, 53130, -177100, 480700, -1081575, 2042975, -3268760, 4457400, -5200300, 5200300, -4457400, 3268760, -2042975, 1081575, -480700, 177100, -53130, 12650, -2300, 300, -25, 1).
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FORMULA
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Sum_{n>=0} 1/a(n) = 45997360927193/23100 - 201753552*Pi^2.
Sum_{n>=0} (-1)^n/a(n) = 16431564019/23100 - 72072*Pi^2. (End)
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MAPLE
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f:=m->[seq( binomial(m+n-1, n)^2-binomial(m+n, n+1)*binomial(m+n-2, n-1), n=0..20)]; f(14);
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MATHEMATICA
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Table[Binomial[13+n, n]^2-Binomial[14+n, n+1]Binomial[12+n, n-1], {n, 0, 20}] (* Harvey P. Dale, Nov 09 2011 *)
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PROG
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(Magma) [(1/13)*Binomial(n+12, 12)^2*(n+13)/(n+1): n in [0..20]]; // Bruno Berselli, Nov 09 2011
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CROSSREFS
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The expression binomial(m+n-1,n)^2-binomial(m+n,n+1)*binomial(m+n-2,n-1) for the values m = 2 through 14 produces the sequences A000012, A000217, A002415, A006542, A006857, A108679, A134288, A134289, A134290, A134291, A140925, A140935, A169937.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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