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A270869
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a(n) = n^5 + 4*n^4 + 13*n^3 + 23*n^2 + 25*n + 3.
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6
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3, 69, 345, 1203, 3351, 7953, 16749, 32175, 57483, 96861, 155553, 239979, 357855, 518313, 732021, 1011303, 1370259, 1824885, 2393193, 3095331, 3953703, 4993089, 6240765, 7726623, 9483291, 11546253, 13953969, 16747995, 19973103, 23677401, 27912453
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OFFSET
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0,1
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LINKS
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FORMULA
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O.g.f.: (3 + 51*x - 24*x^2 + 108*x^3 - 27*x^4 + 9*x^5)/(1-x)^6.
E.g.f.: (3 + 66*x + 105*x^2 + 62*x^3 + 14*x^4 + x^5)*exp(x).
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).
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MATHEMATICA
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Table[n^5 + 4 n^4 + 13 n^3 + 23 n^2 + 25 n + 3, {n, 0, 40}]
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PROG
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(Magma) [n^5+4*n^4+13*n^3+23*n^2+25*n+3: n in [0..40]];
(PARI) x='x+O('x^99); Vec((3+51*x-24*x^2+108*x^3-27*x^4+9*x^5)/(1-x)^6) \\ Altug Alkan, Apr 03 2016
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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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