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A008505 11-dimensional centered tetrahedral numbers. 1
1, 13, 91, 455, 1820, 6188, 18564, 50388, 125970, 293930, 646646, 1352078, 2704155, 5200287, 9657609, 17383405, 30419935, 51889747, 86474661, 141070137, 225666870, 354523390, 547707394, 833099722 (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 (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).

FORMULA

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.

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

MAPLE

seq(binomial(n+12, 12)-binomial(n, 12), n=0..30); # G. C. Greubel, Nov 09 2019

MATHEMATICA

Table[Binomial[n + 12, 12] - Binomial[n, 12], {n, 0, 23}] (* Bruno Berselli, Mar 22 2012 *)

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 *)

PROG

(PARI) vector(31, n, b=binomial; b(n+11, 12) - b(n-1, 12) ) \\ G. C. Greubel, Nov 09 2019

(MAGMA) B:=Binomial; [B(n+12, 12)-B(n, 12): n in [0..30]]; // G. C. Greubel, Nov 09 2019

(Sage) b=binomial; [b(n+12, 12)-b(n, 12) for n in (0..30)] # G. C. Greubel, Nov 09 2019

(GAP) B:=Binomial;; List([0..30], n-> B(n+12, 12)-B(n, 12) ); # G. C. Greubel, Nov 09 2019

CROSSREFS

Sequence in context: A188352 A162631 A247611 * A008495 A010965 A221144

Adjacent sequences:  A008502 A008503 A008504 * A008506 A008507 A008508

KEYWORD

nonn,easy,changed

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified November 21 09:14 EST 2019. Contains 329362 sequences. (Running on oeis4.)