A037953 a(n) = binomial(n, floor((n-5)/2)).
0, 0, 0, 0, 0, 1, 1, 7, 8, 36, 45, 165, 220, 715, 1001, 3003, 4368, 12376, 18564, 50388, 77520, 203490, 319770, 817190, 1307504, 3268760, 5311735, 13037895, 21474180, 51895935, 86493225, 206253075
Offset: 0
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
Programs
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Magma
[Binomial(n, Floor((n-5)/2)): n in [0..40]]; // G. C. Greubel, Jun 21 2022
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Maple
A037953:=n->binomial(n, floor((n-5)/2)); seq(A037953(n), n=0..50); # Wesley Ivan Hurt, Nov 28 2013
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Mathematica
Table[Binomial[n,Floor[(n-5)/2]],{n,0,40}] (* Harvey P. Dale, Oct 11 2012 *) -
PARI
a(n)=binomial(n,(n-5)\2) \\ Charles R Greathouse IV, Oct 23 2023
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SageMath
[binomial(n, (n-5)//2) for n in (0..40)] # G. C. Greubel, Jun 21 2022
Formula
a(n) = binomial(n, A004526(n-5)). - Wesley Ivan Hurt, Nov 28 2013
(n+6)*(n-5)*a(n) = 2*(n)*a(n-1) + 4*(n-1)*n*a(n-2). - R. J. Mathar, Jul 26 2015
From G. C. Greubel, Jun 21 2022: (Start)
G.f.: ((1 +x -6*x^2 -5*x^3 +9*x^4 +5*x^5 -2*x^6) - (1 +x -4*x^2 -3*x^3 +3*x^4 +x^5)*sqrt(1-4*x^2))/(2*x^6*sqrt(1-4*x^2)).
E.g.f.: BesselI(5, 2*x) + BesselI(6, 2*x). (End)