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A247611
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a(n) = Sum_{k=0..6} binomial(12,k)*binomial(n,k).
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3
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1, 13, 91, 455, 1820, 6188, 18564, 49596, 119139, 260743, 527065, 996205, 1778966, 3027038, 4942106, 7785882, 11891061, 17673201, 25643527, 36422659, 50755264, 69525632, 93774176, 124714856, 163753527, 212507211, 272824293, 346805641, 436826650
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: (1 + 6*x + 21*x^2 + 56*x^3 + 126*x^4 + 252*x^5 + 462*x^6) / (1-x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7).
a(n) = (120 - 8042*n + 20581*n^2 - 17380*n^3 + 7645*n^4 -1518*n^5 + 154*n^6)/120.
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MATHEMATICA
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Table[(120 - 8042 n + 20581 n^2 - 17380 n^3 + 7645 n^4 - 1518 n^5 + 154 n^6)/120, {n, 0, 40}] (* or *) CoefficientList[Series[(1 + 6 x + 21 x^2 + 56 x^3 + 126 x^4 + 252 x^5 + 462 x^6)/(1 - x)^7, {x, 0, 40}], x]
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PROG
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(Magma) [(120-8042*n+20581*n^2-17380*n^3+7645*n^4-1518*n^5+ 154*n^6)/120: n in [0..40]]; /* or */ I:=[1, 13, 91, 455, 1820, 6188, 18564]; [n le 7 select I[n] else 7*Self(n-1)-21*Self(n-2)+35*Self(n-3)-35*Self(n-4)+21*Self(n-5)-7*Self(n-6)+Self(n-7): n in [1..40]];
(Sage) m=6; [sum((binomial(2*m, k)*binomial(n, k)) for k in (0..m)) for n in (0..40)] # Bruno Berselli, Sep 22 2014
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CROSSREFS
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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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