A008503 - OEIS

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A008503

9-dimensional centered tetrahedral numbers.

1, 11, 66, 286, 1001, 3003, 8008, 19448, 43758, 92378, 184755, 352705, 646580, 1143780, 1960255, 3265757, 5303727, 8416837, 13079352, 19937632, 29860259, 43999449, 63865594, 91416974

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

FORMULA

G.f.: (1-x^10)/(1-x)^11 = (1+x)*(1+x+x^2+x^3+x^4)*(1-x+x^2-x^3+x^4)/(1-x)^10.

a(n) = (2*n + 1)*(5*n^8 + 20*n^7 + 1370*n^6 + 4040*n^5 + 56549*n^4 + 106388*n^3 + 425916*n^2 + 373392*n + 362880)/362880. [Bruno Berselli, Mar 22 2012]

a(n) = A001287(n+10)-A001287(n). - R. J. Mathar, Aug 10 2013

MAPLE

seq(binomial(n+10, 10)-binomial(n, 10), n=0..30); # G. C. Greubel, Nov 09 2019

MATHEMATICA

Table[Binomial[n + 10, 10] - Binomial[n, 10], {n, 0, 23}] (* Bruno Berselli, Mar 22 2012 *)

PROG

(PARI) vector(31, n, b=binomial; b(n+9, 10) - b(n-1, 10) ) \\ G. C. Greubel, Nov 09 2019

(Magma) B:=Binomial; [B(n+10, 10)-B(n, 10): n in [0..30]]; // G. C. Greubel, Nov 09 2019

(Sage) b=binomial; [b(n+10, 10)-b(n, 10) for n in (0..30)] # G. C. Greubel, Nov 09 2019

(GAP) B:=Binomial;; List([0..30], n-> B(n+10, 10)-B(n, 10) ); # G. C. Greubel, Nov 09 2019

CROSSREFS

Sequence in context: A331715 A162628 A247610 * A008493 A001287 A229891

Adjacent sequences: A008500 A008501 A008502 * A008504 A008505 A008506

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved