A163279 a(n) = (n^6 + 2n^5 + 2n^4 + n^3 + 2n)/2.

4, 86, 705, 3364, 11630, 32514, 78211, 168200, 331704, 610510, 1062149, 1763436, 2814370, 4342394, 6507015, 9504784, 13574636, 19003590, 26132809, 35364020, 47166294, 62083186, 80740235, 103852824, 132234400, 166805054, 208600461

Offset: 1

Author

Omar E. Pol, Nov 07 2009

Keywords

• easy
• nonn

Comments

Before this sequence, a(5) = 11630 was an uninteresting number, see Links section. - Omar E. Pol, Apr 25 2016

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..1000
• Charles R Greathouse IV, Uninteresting numbers
• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Crossrefs

Cf. A000290, A002378, A035287.

Programs

MATLAB

for n=1:354 a(n) = n^2*((n*(n+1))^2 + n*(n+1) + 2/n)/2; end
% Kyle Stern, Jan 05 2010

Mathematica

Array[Function[n, (n^6 + 2 n^5 + 2 n^4 + n^3 + 2 n)/2], {27}] (* or *)
Rest@ CoefficientList[Series[x (4 + 58 x + 187 x^2 + 95 x^3 + 17 x^4 - x^5)/(1 - x)^7, {x, 0, 27}], x] (* Michael De Vlieger, Apr 25 2016 *)
LinearRecurrence[{7,-21,35,-35,21,-7,1},{4,86,705,3364,11630,32514,78211},30] (* Harvey P. Dale, Mar 08 2018 *)

PARI

a(n)=(n^6+n^3)/2+n^5+n^4+n \\ Charles R Greathouse IV, Jul 29 2011

Formula

G.f.: x*(4 + 58*x + 187*x^2 + 95*x^3 + 17*x^4 - x^5)/(1 - x)^7. - Ilya Gutkovskiy, Apr 25 2016

Extensions

More terms from Kyle Stern, Jan 05 2010