A037951 a(n) = binomial(n, floor((n-3)/2)).

0, 0, 0, 1, 1, 5, 6, 21, 28, 84, 120, 330, 495, 1287, 2002, 5005, 8008, 19448, 31824, 75582, 125970, 293930, 497420, 1144066, 1961256, 4457400, 7726160, 17383860, 30421755, 67863915, 119759850, 265182525

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A035952, A035953, A035954, A035955, A035956, A035957.

Cf. A089940, A101491.

Programs

Magma

[Binomial(n, Floor((n-3)/2)): n in [0..40]]; // G. C. Greubel, Jun 21 2022

Mathematica

Table[Binomial[n,Floor[(n-3)/2]],{n,0,40}] (* Harvey P. Dale, Jul 09 2017 *)

SageMath

[binomial(n, (n-3)//2) for n in (0..40)] # G. C. Greubel, Jun 21 2022

Formula

E.g.f.: Bessel_I(3, 2*x) + Bessel_I(4, 2*x) - Paul Barry, Feb 28 2006

(n+4)*(n-3)*a(n) = (-n^2+3*n+12)*a(n-1) + 2*(2*n+1)*(n-1)*a(n-2) + 4*(n-1)*(n-2)*a(n-3). - R. J. Mathar, Nov 24 2012

G.f.: ((1 +x -4*x^2 -3*x^3 +2*x^4) - (1 +x -2*x^2 -x^3)*sqrt(1-4*x^2))/(2*x^4*sqrt(1-4*x^2)). - G. C. Greubel, Jun 21 2022