A188480 - OEIS

%I #28 Sep 06 2023 16:14:39

%S 1,10,39,99,203,366,605,939,1389,1978,2731,3675,4839,6254,7953,9971,

%T 12345,15114,18319,22003,26211,30990,36389,42459,49253,56826,65235,

%U 74539,84799,96078,108441,121955,136689,152714,170103,188931

%N a(n) = (n^4 + 16*n^3 + 65*n^2 + 26*n + 12)/12.

%C Third column of number triangle A188461.

%H Vincenzo Librandi, <a href="/A188480/b188480.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

%F G.f.: (1 + 5*x - x^2 - 6*x^3 + 3*x^4)/(1-x)^5.

%F E.g.f.: exp(x)*(12 + 108*x + 120*x^2 + 22*x^3 + x^4)/12. - _Stefano Spezia_, Sep 06 2023

%t Table[(n^4+16n^3+65n^2+26n+12)/12,{n,0,40}] (* or *) LinearRecurrence[ {5,-10,10,-5,1},{1,10,39,99,203},40] (* _Harvey P. Dale_, Jan 23 2016 *)

%o (Magma) [(n^4+16*n^3+65*n^2+26*n+12)/12: n in [0..90]]; // _Vincenzo Librandi_, Apr 05 2011

%o (PARI) a(n)=1+(n^4+16*n^3+65*n^2+26*n)/12 \\ _Charles R Greathouse IV_, May 04 2011

%Y Cf. A188461.

%K nonn,easy

%O 0,2

%A _Paul Barry_, Apr 01 2011