%I #27 Sep 08 2022 08:44:35
%S 1,10,55,220,715,2002,5005,11440,24310,48619,92368,167905,293710,
%T 496705,815188,1302499,2031535,3100240,4638205,6814522,9847045,
%U 14013220,19662655,27231610,37259596
%N 8-dimensional centered tetrahedral numbers.
%H Bruno Berselli, <a href="/A008502/b008502.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 G.f.: (1-x^9 )/(1-x)^10 = (1+x+x^2)*(1+x^3+x^6) / (1-x)^9.
%F a(n) = 1 + n*(n+1)*(3*n^6+9*n^5+509*n^4+1003*n^3+11464*n^2+10964*n +36528)/13440. - _R. J. Mathar_, Nov 02 2011
%p seq(binomial(n+9,9)-binomial(n,9), n=0..30); # _G. C. Greubel_, Nov 09 2019
%t Table[Binomial[n + 9, 9] - Binomial[n, 9], {n, 0, 24}] (* _Bruno Berselli_, Mar 22 2012 *)
%t LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1}, {1,10,55,220,715,2002, 5005,11440,24310},30] (* _Harvey P. Dale_, Jan 17 2016 *)
%o (PARI) vector(31, n, b=binomial; b(n+8,9) - b(n-1,9) ) \\ _G. C. Greubel_, Nov 09 2019
%o (Magma) B:=Binomial; [B(n+9,9)-B(n,9): n in [0..30]]; // _G. C. Greubel_, Nov 09 2019
%o (Sage) b=binomial; [b(n+9,9)-b(n,9) for n in (0..30)] # _G. C. Greubel_, Nov 09 2019
%o (GAP) B:=Binomial;; List([0..30], n-> B(n+9,9)-B(n,9) ); # _G. C. Greubel_, Nov 09 2019
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_