A008506 12-dimensional centered tetrahedral numbers.

1, 14, 105, 560, 2380, 8568, 27132, 77520, 203490, 497420, 1144066, 2496144, 5200300, 10400599, 20058286, 37442055, 67863355, 119757470, 206244507, 347346468, 573088920, 927780270, 1475840380, 2309645534, 3559971156, 5409749996

Offset

0,2

Links

Bruno Berselli, Table of n, a(n) for n = 0..1000

Milan Janjic, Two Enumerative Functions

Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).

Formula

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.

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

Maple

seq(binomial(n+13, 13)-binomial(n, 13), n=0..30); # G. C. Greubel, Nov 09 2019

Mathematica

Table[Binomial[n + 13, 13] - Binomial[n, 13], {n, 0, 22}] (* Bruno Berselli, Mar 22 2012 *)

Prog

(Python)
A008506_list, m = [], [13, -65, 221, -494, 793, -923, 793, -494, 221, -65, 13, 0, 1]
for _ in range(10**2):
    A008506_list.append(m[-1])
    for i in range(12):
        m[i+1] += m[i] # Chai Wah Wu, Dec 15 2015
(Magma) [Binomial(n+13, 13) - Binomial(n, 13): n in [0..30]]; // Vincenzo Librandi, Dec 16 2015
(PARI) vector(31, n, b=binomial; b(n+13, 13) - b(n-1, 13) ) \\ G. C. Greubel, Nov 09 2019
(Sage) b=binomial; [b(n+13, 13)-b(n, 13) for n in (0..30)] # G. C. Greubel, Nov 09 2019
(GAP) B:=Binomial;; List([0..30], n-> B(n+13, 13)-B(n, 13) ); # G. C. Greubel, Nov 09 2019

Crossrefs

Sequence in context: A068390 A162632 A220893 * A010966 A290895 A341226

Adjacent sequences: A008503 A008504 A008505 * A008507 A008508 A008509

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved