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1, 12, 57, 182, 462, 1008, 1974, 3564, 6039, 9724, 15015, 22386, 32396, 45696, 63036, 85272, 113373, 148428, 191653, 244398, 308154, 384560, 475410, 582660, 708435, 855036, 1024947, 1220842, 1445592, 1702272, 1994168, 2324784, 2697849, 3117324, 3587409
(list;
graph;
refs;
listen;
history;
text;
internal format)
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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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A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
Herbert John Ryser, Combinatorial Mathematics, "The Carus Mathematical Monographs", No. 14, John Wiley and Sons, 1963, pp. 1-16.
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LINKS
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FORMULA
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a(n) = C(n+4, 4)*(7*n+5)/5.
G.f.: (1+6*x)/(1-x)^6.
a(n) = 6*a(n-1) -15*a(n-2) +20*a(n-3) -15*a(n-4) +6*a(n-5) -a(n-6).
a(n) = (n+1)*(n+2)*(n+3)*(n+4)*(7*n+5)/120. (End)
E.g.f.: (5! +1320*x +2040*x^2 +920*x^3 +145*x^4 +7*x^5)*exp(x)/5!
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MAPLE
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MATHEMATICA
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Table[(n+1)(n+2)(n+3)(n+4)(7n+5)/120, {n, 0, 40}] (* Vincenzo Librandi, May 03 2015 *)
LinearRecurrence[{6, -15, 20, -15, 6, -1}, {1, 12, 57, 182, 462, 1008}, 40] (* Harvey P. Dale, May 05 2022 *)
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PROG
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(Magma) [(n+1)*(n+2)*(n+3)*(n+4)*(7*n+5)/120 : n in [0..40]]; // Wesley Ivan Hurt, May 02 2015
(PARI) vector(40, n, (7*n-2)*binomial(n+3, 4)/5) \\ G. C. Greubel, Aug 29 2019
(Sage) [(7*n+5)*binomial(n+4, 4)/5 for n in (0..40)] # G. C. Greubel, Aug 29 2019
(GAP) List([0..40], n-> (7*n+5)*Binomial(n+4, 4)/5); # G. C. Greubel, Aug 29 2019
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CROSSREFS
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Cf. A093564 ((7, 1) Pascal, column m=5).
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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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