%I #25 Sep 08 2022 08:44:35
%S 1,13,91,455,1820,6188,18564,50388,125970,293930,646646,1352078,
%T 2704155,5200287,9657609,17383405,30419935,51889747,86474661,
%U 141070137,225666870,354523390,547707394,833099722
%N 11-dimensional centered tetrahedral numbers.
%H Bruno Berselli, <a href="/A008505/b008505.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).
%F G.f.: (1-x^12)/(1-x)^13 = (1+x)*(1+x^2)*(1-x+x^2)*(1+x+x^2)*(1-x^2+x^4)/(1-x)^12.
%F a(n) = (2*n+1)*(3*n^10 +15*n^9 +1835*n^8 +7250*n^7 +195629*n^6 +561575*n^5 +4970585*n^4 +9013640*n^3 +28095948*n^2 +23681520*n +19958400)/19958400. - _Bruno Berselli_, Mar 22 2012
%p seq(binomial(n+12,12)-binomial(n,12), n=0..30); # _G. C. Greubel_, Nov 09 2019
%t Table[Binomial[n + 12, 12] - Binomial[n, 12], {n, 0, 23}] (* _Bruno Berselli_, Mar 22 2012 *)
%t LinearRecurrence[{12,-66,220,-495,792,-924,792,-495,220,-66,12,-1}, {1, 13, 91,455,1820,6188,18564,50388,125970,293930,646646,1352078},20] (* _Harvey P. Dale_, May 06 2014 *)
%o (PARI) vector(31, n, b=binomial; b(n+11,12) - b(n-1,12) ) \\ _G. C. Greubel_, Nov 09 2019
%o (Magma) B:=Binomial; [B(n+12,12)-B(n,12): n in [0..30]]; // _G. C. Greubel_, Nov 09 2019
%o (Sage) b=binomial; [b(n+12,12)-b(n,12) for n in (0..30)] # _G. C. Greubel_, Nov 09 2019
%o (GAP) B:=Binomial;; List([0..30], n-> B(n+12,12)-B(n,12) ); # _G. C. Greubel_, Nov 09 2019
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_