OFFSET
5,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 5..1000
Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
FORMULA
a(n) = Sum_{k=0..4} binomial(n-k, 9-2*k). - Len Smiley, Oct 20 2001
a(n) = C(n,n-1) + C(n+1,n-2) + C(n+2,n-3) + C(n+3,n-4) + C(n+4,n-5), n>=1 . - Zerinvary Lajos, May 29 2007
G.f.: x^5*(1 -7*x +23*x^2 -44*x^3 +55*x^4 -44*x^5 +23*x^6 -7*x^7 +x^8) / (1-x)^10 . - R. J. Mathar, Oct 31 2015
MAPLE
A027932 := proc(n)
1/362880 *(n-4) *(n^8 -32*n^7 +490*n^6 -4592*n^5 +30289*n^4 -147728*n^3 +543780*n^2 -1359648*n +1905120)
end proc:
seq(A027932(n), n=5..30) ; # R. J. Mathar, Jun 29 2012
MATHEMATICA
Sum[Binomial[Range[5, 40] -k, 9-2*k], {k, 0, 4}] (* G. C. Greubel, Sep 27 2019 *)
PROG
(PARI) vector(40, n, sum(k=0, 4, binomial(n+4-k, 9-2*k)) ) \\ G. C. Greubel, Sep 27 2019
(Magma) [&+[Binomial(n-k, 9-2*k): k in [0..4]] : n in [5..40]]; // G. C. Greubel, Sep 27 2019
(Sage) [sum(binomial(n-k, 9-2*k) for k in (0..4)) for n in (5..40)] # G. C. Greubel, Sep 27 2019
(GAP) List([5..40], n-> Sum([0..4], k-> Binomial(n-k, 9-2*k)) ); # G. C. Greubel, Sep 27 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved