%I #27 Feb 07 2024 11:29:54
%S 1,12,78,364,1365,4368,12376,31824,75582,167960,352716,705431,1352066,
%T 2496066,4457036,7724795,13033527,21461804,34565466,54551718,84504355,
%U 128671764,192831288,284745682
%N 10-dimensional centered tetrahedral numbers.
%H Bruno Berselli, <a href="/A008504/b008504.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
%F G.f.: (1-x^11)/(1-x)^12 = (1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10)/(1-x)^11.
%F a(n) = 1 + 11*n*(n+1)*(n^8 +4*n^7 +416*n^6 +1234*n^5 +28019*n^4 +53986*n^3 +395644*n^2 +368856*n +966240)/3628800. - _Bruno Berselli_, Mar 22 2012
%p seq(binomial(n+11,11)-binomial(n,11), n=0..30); # _G. C. Greubel_, Nov 09 2019
%t Table[Binomial[n + 11, 11] - Binomial[n, 11], {n, 0, 23}] (* _Bruno Berselli_, Mar 22 2012 *)
%t LinearRecurrence[{11,-55,165,-330,462,-462,330,-165,55,-11,1},{1,12,78,364,1365,4368,12376,31824,75582,167960,352716},30] (* _Harvey P. Dale_, Dec 25 2023 *)
%o (PARI) vector(31, n, b=binomial; b(n+10,11) - b(n-1,11) ) \\ _G. C. Greubel_, Nov 09 2019
%o (Magma) B:=Binomial; [B(n+11,11)-B(n,11): n in [0..30]]; // _G. C. Greubel_, Nov 09 2019
%o (Sage) b=binomial; [b(n+11,11)-b(n,11) for n in (0..30)] # _G. C. Greubel_, Nov 09 2019
%o (GAP) B:=Binomial;; List([0..30], n-> B(n+11,11)-B(n,11) ); # _G. C. Greubel_, Nov 09 2019
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_