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]
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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved