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A034265
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a(n) = binomial(n+6,6)*(6*n+7)/7.
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7
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1, 13, 76, 300, 930, 2442, 5676, 12012, 23595, 43615, 76648, 129064, 209508, 329460, 503880, 751944, 1097877, 1571889, 2211220, 3061300, 4177030, 5624190, 7480980, 9839700, 12808575, 16513731, 21101328, 26739856, 33622600, 41970280
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OFFSET
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0,2
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REFERENCES
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A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
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LINKS
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FORMULA
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G.f.: (1+5*x)/(1-x)^8.
a(0)=1, a(1)=13, a(2)=76, a(3)=300, a(4)=930, a(5)=2442, a(6)=5676, a(7)=12012, a(n) = 8*a(n-1) -28*a(n-2) +56*a(n-3) -70*a(n-4) +56*a(n-5) -28*a(n-6) +8*a(n-7) -a(n-8). - Harvey P. Dale, Jul 29 2014
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MAPLE
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seq((6*n+7)*binomial(n+6, 6)/7, n=0..30); # G. C. Greubel, Aug 28 2019
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MATHEMATICA
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Accumulate[Table[(n+1)Binomial[n+5, 5], {n, 0, 30}]] (* or *) LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {1, 13, 76, 300, 930, 2442, 5676, 12012}, 30] (* Harvey P. Dale, Jul 29 2014 *)
CoefficientList[Series[(1+5x)/(1-x)^8, {x, 0, 40}], x] (* Vincenzo Librandi, Jul 30 2014 *)
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PROG
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(Magma) [(6*n+7)*Binomial(n+6, 6)/7: n in [0..40]]; // Vincenzo Librandi, Jul 30 2014
(Sage) [(6*n+7)*binomial(n+6, 6)/7 for n in (0..30)] # G. C. Greubel, Aug 28 2019
(GAP) List([0..30], n-> (6*n+7)*Binomial(n+6, 6)/7); # G. C. Greubel, Aug 28 2019
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CROSSREFS
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a(n)=f(n, 5) where f is given in A034261.
Cf. A093563 ((6, 1) Pascal, column m=7).
Cf. similar sequences listed in A254142.
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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