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A061224
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a(n) = n^2 + (n + 1)^3 + (n + 2)^4 + (n + 3)^5.
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1
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260, 1114, 3412, 8474, 18244, 35410, 63524, 107122, 171844, 264554, 393460, 568234, 800132, 1102114, 1488964, 1977410, 2586244, 3336442, 4251284, 5356474, 6680260, 8253554, 10110052, 12286354, 14822084, 17760010, 21146164, 25029962
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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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G.f.: 2*(130 - 223*x + 314*x^2 - 244*x^3 + 100*x^4 - 17*x^5)/(1-x)^6. - Bruno Berselli, Aug 05 2011
E.g.f.: exp(x)*(260 + 854*x + 722*x^2 + 220*x^3 + 26*x^4 + x^5). - Stefano Spezia, Nov 02 2018
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EXAMPLE
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a(1) = 1 + 2^3 + 3^4 + 4^5 = 1 + 8 + 81 + 1024 = 1114.
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MAPLE
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seq(n^2+(n+1)^3+(n+2)^4+(n+3)^5, n=0..30); # Muniru A Asiru, Nov 02 2018
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MATHEMATICA
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Table[n^2 +(n+1)^3 +(n+2)^4 +(n+3)^5, {n, 0, 30}] (* G. C. Greubel, Nov 02 2018 *)
CoefficientList[Series[E^x (260 + 854 x + 722 x^2 + 220 x^3 + 26 x^4 + x^5), {x, 0, 50}], x]*Table[k!, {k, 0, 50}] (* Stefano Spezia, Nov 02 2018 *)
Table[260+440 n+298 n^2+99 n^3+16 n^4+n^5, {n, 0, 30}] (* or *) LinearRecurrence[ {6, -15, 20, -15, 6, -1}, {260, 1114, 3412, 8474, 18244, 35410}, 30] (* Harvey P. Dale, Nov 14 2022 *)
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PROG
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(Magma) [n^2 + (n + 1)^3 + (n + 2)^4 + (n + 3)^5: n in [0..30]]; // Vincenzo Librandi, Aug 05 2011
(PARI) vector(30, n, n--; n^2 +(n+1)^3 +(n+2)^4 +(n+3)^5) \\ G. C. Greubel, Nov 02 2018
(GAP) List([0..30], n->n^2+(n+1)^3+(n+2)^4+(n+3)^5); # Muniru A Asiru, Nov 02 2018
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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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EXTENSIONS
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STATUS
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approved
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