The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #33 Sep 08 2022 08:46:01
%S 1,28,1537,21322,145633,659176,2284273,6565462,16434817,36993268,
%T 76543201,147907618,270071137,470178112,785923153,1268369326,
%U 1985229313,3024644812,4499499457,6552300538,9360664801,13143443608,18167522737
%N a(n) = 1 + 2*n^2 + 3*n^3 + 4*n^4 +5*n^5 + 6*n^6 + 7*n^7.
%H G. C. Greubel, <a href="/A209265/b209265.txt">Table of n, a(n) for n = 0..5000</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-1).
%F 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
%e a(2) = 1 + 2*2^2 + 3*2^3 + 4*2^4 +5*2^5 + 6*2^6 + 7*2^7 = 1537.
%t 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 *)
%o (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 */
%o (PARI) for(n=0,30, print1(1 + sum(k=2,7, k*n^k), ", ")) \\ _G. C. Greubel_, Jan 05 2018
%o (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
%Y Cf. A209262, A209263, A209264.
%K nonn,easy
%O 0,2
%A _Jonathan Vos Post_, Jan 14 2013