OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).
FORMULA
a(n) = A000581(n) + A000580(n) + A000579(n) + A000389(n) + A000332(n) + A000292(n) + A000217(n) + n. a(n) = A000581(n) + A116082(n).
G.f. ( -x*(2*x^2 - 2*x + 1)*(2*x^4 - 4*x^3 + 6*x^2 - 4*x + 1) ) / (x-1)^9. - R. J. Mathar, Oct 21 2011
a(n) = n*(n+1)*(25584 - 9604*n + 5264*n^2 - 1295*n^3 + 231*n^4 - 21*n^5 + n^6)/40320. - G. C. Greubel, Nov 25 2017
MAPLE
seq(sum(binomial(n, k), k=1..8), n=0..33); # Zerinvary Lajos, Dec 14 2007
MATHEMATICA
Table[n*(n + 1)*(25584 - 9604*n + 5264*n^2 - 1295*n^3 + 231*n^4 - 21*n^5 + n^6)/40320, {n, 0, 50}] (* G. C. Greubel, Nov 25 2017 *)
Table[Total[Binomial[n, Range[8]]], {n, 0, 40}] (* Harvey P. Dale, Aug 14 2023 *)
PROG
(Sage) [binomial(n, 2)+binomial(n, 4)+binomial(n, 6)+binomial(n, 8) for n in range(1, 35)] # Zerinvary Lajos, May 17 2009
(Sage) [binomial(n, 2)+binomial(n, 4)+binomial(n, 6)+binomial(n, 8)+binomial(n, 1)+binomial(n, 3)+binomial(n, 5)+binomial(n, 7)for n in range(0, 34)] # Zerinvary Lajos, May 17 2009
(PARI) for(n=0, 30, print1(n*(n+1)*(25584 - 9604*n + 5264*n^2 - 1295*n^3 + 231*n^4 - 21*n^5 + n^6 ) /40320, ", ")) \\ G. C. Greubel, Nov 25 2017
(Magma) [n*(n+1)*(25584 - 9604*n + 5264*n^2 - 1295*n^3 + 231*n^4 - 21*n^5 + n^6 ) /40320: n in [0..30]]; // G. C. Greubel, Nov 25 2017
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Mar 15 2006
STATUS
approved