%I #14 Sep 08 2022 08:45:12

%S 0,11,37,85,163,280,446,672,970,1353,1835,2431,3157,4030,5068,6290,

%T 7716,9367,11265,13433,15895,18676,21802,25300,29198,33525,38311,

%U 43587,49385,55738,62680,70246,78472,87395,97053,107485,118731,130832,143830,157768

%N a(n) = (1/24)*(n+1)*(n+3)*(n^2+22*n+88).

%H G. C. Greubel, <a href="/A090950/b090950.txt">Table of n, a(n) for n = -1..1000</a>

%H P. Erdős, R. K. Guy and J. W. Moon, <a href="http://jlms.oxfordjournals.org/content/s2-9/4/565.extract">On refining partitions</a>, J. London Math. Soc., 9 (1975), 565-570.

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

%F From _G. C. Greubel_, Feb 04 2019: (Start)

%F G.f.: (11 -18*x +10*x^2 -2*x^3)/(1-x)^5.

%F E.g.f.: (264 +624*x +264*x^2 +32*x^3 +x^4)*exp(x)/24. (End)

%p A090950:=n->(1/24)*(n+1)*(n+3)*(n^2+22*n+88): seq(A090950(n), n=-1..80); # _Wesley Ivan Hurt_, Apr 26 2017

%t Table[(n+1)*(n+3)*(n^2+22*n+88)/24, {n,-1,30}] (* _G. C. Greubel_, Feb 04 2019 *)

%o (PARI) a(n) = (n+1)*(n+3)*(n^2+22*n+88)/24; \\ _Michel Marcus_, Jan 12 2016

%o (Magma) [(n+1)*(n+3)*(n^2+22*n+88)/24: n in [-1..30]]; // _G. C. Greubel_, Feb 04 2019

%o (Sage) [(n+1)*(n+3)*(n^2+22*n+88)/24 for n in (-1..30)] # _G. C. Greubel_, Feb 04 2019

%o (GAP) List([-1..30], n -> (n+1)*(n+3)*(n^2+22*n+88)/24); # _G. C. Greubel_, Feb 04 2019

%K nonn,easy

%O -1,2

%A _N. J. A. Sloane_, Feb 28 2004