A209265 a(n) = 1 + 2*n^2 + 3*n^3 + 4*n^4 +5*n^5 + 6*n^6 + 7*n^7.

1, 28, 1537, 21322, 145633, 659176, 2284273, 6565462, 16434817, 36993268, 76543201, 147907618, 270071137, 470178112, 785923153, 1268369326, 1985229313, 3024644812, 4499499457, 6552300538, 9360664801, 13143443608, 18167522737

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Formula

G.f.: ( 1 + 20*x + 1341*x^2 + 9754*x^3 + 16595*x^4 + 6960*x^5 + 607*x^6 + 2*x^7 ) / (1-x)^8. - R. J. Mathar, Jan 22 2013

Example

a(2) = 1 + 2*2^2 + 3*2^3 + 4*2^4 +5*2^5 + 6*2^6 + 7*2^7 = 1537.

Mathematica

Table[Total[Table[i*n^i, {i, 2, 7}]]+1, {n, 0, 30}] (* or *) LinearRecurrence[ {8, -28, 56, -70, 56, -28, 8, -1}, {1, 28, 1537, 21322, 145633, 659176, 2284273, 6565462}, 30] (* Harvey P. Dale, Sep 26 2016 *)

Prog

(Maxima) makelist(1 + 2*n^2 + 3*n^3 + 4*n^4 +5*n^5 + 6*n^6 + 7*n^7, n, 0, 20); /* Martin Ettl, Jan 25 2013 */
(PARI) for(n=0, 30, print1(1 + sum(k=2, 7, k*n^k), ", ")) \\ G. C. Greubel, Jan 05 2018
(Magma) [1 + 2*n^2 + 3*n^3 + 4*n^4 + 5*n^5 + 6*n^6 + 7*n^7: n in [0..30]]; // G. C. Greubel, Jan 05 2018

Crossrefs

Cf. A209262, A209263, A209264.

Sequence in context: A013926 A110696 A007222 * A042515 A042512 A285029

Adjacent sequences: A209262 A209263 A209264 * A209266 A209267 A209268

Keyword

nonn,easy

Author

Jonathan Vos Post, Jan 14 2013

Status

approved