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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved