A027932 T(n, 2n-9), T given by A027926.

1, 3, 8, 21, 55, 143, 364, 894, 2098, 4685, 9955, 20175, 39130, 72905, 130965, 227612, 383911, 630191, 1009242, 1580345, 2424289, 3649547, 5399802, 7863034, 11282400, 15969161, 22317933, 30824563, 42106956, 56929205

Offset: 5

Author

Clark Kimberling

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A228074.

Programs

GAP

List([5..40], n-> Sum([0..4], k-> Binomial(n-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

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 *)

PARI

vector(40, n, sum(k=0,4, binomial(n+4-k, 9-2*k)) ) \\ 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

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