%I #35 Sep 08 2022 08:44:35
%S 1,14,105,560,2380,8568,27132,77520,203490,497420,1144066,2496144,
%T 5200300,10400599,20058286,37442055,67863355,119757470,206244507,
%U 347346468,573088920,927780270,1475840380,2309645534,3559971156,5409749996
%N 12-dimensional centered tetrahedral numbers.
%H Bruno Berselli, <a href="/A008506/b008506.txt">Table of n, a(n) for n = 0..1000</a>
%H Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Two Enumerative Functions</a>
%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).
%F G.f.: (1-x^13)/(1-x)^14 = (1 +x +x^2 +x^3 +x^4 +x^5 +x^6 +x^7 +x^8 +x^9 +x^10 +x^11 +x^12)/(1-x)^13.
%F a(n) = 1 + 13*n*(n+1)*(n^10 +5*n^9 +864*n^8 +3426*n^7 +136197*n^6 +396621*n^5 +5502866*n^4 +10348684*n^3 +56939592*n^2 +51830784*n +114341760)/479001600. - _Bruno Berselli_, Mar 22 2012
%p seq(binomial(n+13,13)-binomial(n,13), n=0..30); # _G. C. Greubel_, Nov 09 2019
%t Table[Binomial[n + 13, 13] - Binomial[n, 13], {n, 0, 22}] (* _Bruno Berselli_, Mar 22 2012 *)
%o (Python)
%o A008506_list, m = [], [13, -65, 221, -494, 793, -923, 793, -494, 221, -65, 13, 0, 1]
%o for _ in range(10**2):
%o A008506_list.append(m[-1])
%o for i in range(12):
%o m[i+1] += m[i] # _Chai Wah Wu_, Dec 15 2015
%o (Magma) [Binomial(n+13,13) - Binomial(n, 13): n in [0..30]]; // _Vincenzo Librandi_, Dec 16 2015
%o (PARI) vector(31, n, b=binomial; b(n+13,13) - b(n-1,13) ) \\ _G. C. Greubel_, Nov 09 2019
%o (Sage) b=binomial; [b(n+13,13)-b(n,13) for n in (0..30)] # _G. C. Greubel_, Nov 09 2019
%o (GAP) B:=Binomial;; List([0..30], n-> B(n+13,13)-B(n,13) ); # _G. C. Greubel_, Nov 09 2019
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_