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1, 15, 92, 372, 1170, 3102, 7260, 15444, 30459, 56485, 99528, 167960, 273156, 430236, 658920, 984504, 1438965, 2062203, 2903428, 4022700, 5492630, 7400250, 9849060, 12961260, 16880175, 21772881, 27833040, 35283952, 44381832, 55419320, 68729232, 84688560, 103722729, 126310119
(list;
graph;
refs;
listen;
history;
text;
internal format)
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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.
Murray R. Spiegel, Calculus of Finite Differences and Difference Equations, "Schaum's Outline Series", McGraw-Hill, 1971, pp. 10-20, 79-94.
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LINKS
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FORMULA
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a(n) = (8*n+7)*C(n+6, 6)/7.
G.f.: (1+7*x)/(1-x)^8.
E.g.f.: (5040 +70560*x +158760*x^2 +117600*x^3 +36750*x^4 +5292*x^5 +343*x^6 +8*x^7)*exp(x)/5040. - G. C. Greubel, Aug 29 2019
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MAPLE
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seq((8*n+7)*Binomial(n+6, 6)/7, n=0..40); # G. C. Greubel, Aug 29 2019
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MATHEMATICA
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Table[(8*n+7)*Binomial[n+6, 6]/7, {n, 0, 40}] (* G. C. Greubel, Aug 29 2019 *)
LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {1, 15, 92, 372, 1170, 3102, 7260, 15444}, 40] (* Harvey P. Dale, Aug 12 2021 *)
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PROG
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(PARI) vector(40, n, (8*n-1)*binomial(n+5, 6)/7) \\ G. C. Greubel, Aug 29 2019
(Magma) [(8*n+7)*Binomial(n+6, 6)/7: n in [0..40]]; // G. C. Greubel, Aug 29 2019
(Sage) [(8*n+7)*binomial(n+6, 6)/7 for n in (0..40)] # G. C. Greubel, Aug 29 2019
(GAP) List([0..40], n-> (8*n+7)*Binomial(n+6, 6)/7); # G. C. Greubel, Aug 29 2019
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CROSSREFS
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Cf. A093565 ((8, 1) Pascal, column m=7).
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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