%I #8 May 27 2016 20:58:24
%S 0,3,31,251,1485,6665,24073,73486,196626,473595,1047255,2157793,
%T 4189991,7736001,13676705,23285020,38354788,61359171,95642751,
%U 145651815,217207585,317827433,457099401,647115626,902970550,1243330075,1691078103,2274047181
%N P(P(n)) - P(P(n-1)), where P(n) = (n+1)*(n+2)*(n+3)/6 (see A000292).
%H G. C. Greubel, <a href="/A111400/b111400.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9, -36, 84, -126, 126, -84, 36, -9, 1).
%F From _Chai Wah Wu_, May 27 2016: (Start)
%F a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9).
%F G.f.: x*(x^6 - 8*x^5 + 110*x^4 + 90*x^3 + 80*x^2 + 4*x + 3)/(1 - x)^9. (End)
%t LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {0, 3, 31,
%t 251, 1485, 6665, 24073, 73486, 196626}, 100] (* _G. C. Greubel_, May 27 2016 *)
%Y Cf. A113596, A000292.
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Nov 11 2005