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A055822
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a(n) = T(n, n-5), array T as in A055818.
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9
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1, 47, 144, 328, 640, 1131, 1863, 2910, 4359, 6311, 8882, 12204, 16426, 21715, 28257, 36258, 45945, 57567, 71396, 87728, 106884, 129211, 155083, 184902, 219099, 258135, 302502, 352724, 409358, 472995, 544261, 623818, 712365, 810639, 919416, 1039512, 1171784
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OFFSET
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5,2
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LINKS
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FORMULA
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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) for n > 11.
G.f.: x^5*(1 + 41*x -123*x^2 + 149*x^3 - 93*x^4 + 30*x^5 - 4*x^6)/(1-x)^6. (End)
a(n) = (480 +524*n -250*n^2 -45*n^3 +10*n^4 +n^5)/120, for n>5, with a(5) = 1.
E.g.f.: (-480 -720*x -180*x^2 +60*x^3 +30*x^4 -4*x^5 + (480 +240*x -300*x^2 + 40*x^3 +20*x^4 +x^5)*exp(x))/120. (End)
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MAPLE
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seq( `if`(n=5, 1, (480 +524*n -250*n^2 -45*n^3 +10*n^4 +n^5)/120), n=5..50); # G. C. Greubel, Jan 22 2020
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MATHEMATICA
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Join[{1, 47, 144, 328, 640}, LinearRecurrence[{6, -15, 20, -15, 6, -1}, {1131, 1863, 2910, 4359, 6311, 8882}, 5004]] (* Vincenzo Librandi, Dec 30 2016 *)
Table[If[n==5, 1, (480 +524*n -250*n^2 -45*n^3 +10*n^4 +n^5)/120], {n, 5, 50}] (* G. C. Greubel, Jan 22 2020 *)
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PROG
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(Magma) I:=[1, 47, 144, 328, 640, 1131, 1863, 2910, 4359, 6311, 8882]; [n le 11 select I[n] else 6*Self(n-1)-15*Self(n-2) +20*Self(n-3)-15*Self(n-4)+6*Self(n-5)-Self(n-6): n in [1..50]]; // Vincenzo Librandi, Dec 30 2016
(PARI) vector(45, n, my(m=n+4); if(m==5, 1, (480 +524*m -250*m^2 -45*m^3 +10*m^4 +m^5)/120)) \\ G. C. Greubel, Jan 22 2020
(Sage) [1]+[(480 +524*n -250*n^2 -45*n^3 +10*n^4 +n^5)/120 for n in (6..50)] # G. C. Greubel, Jan 22 2020
(GAP) Concatenation([1], List([6..50], n-> (480 +524*n -250*n^2 -45*n^3 +10*n^4 +n^5)/120 )); # G. C. Greubel, Jan 22 2020
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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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