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A037964 a(n) = binomial(4*n,2*n)/2 - (-1)^n*binomial(2*n,n)/2. 3
0, 4, 32, 472, 6400, 92504, 1351616, 20060016, 300533760, 4537591960, 68923172032, 1052049834576, 16123800489472, 247959271674352, 3824345280321920, 59132290859989472, 916312070170755072 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

The right-hand side of a binomial coefficient identity in H. W. Gould, Combinatorial Identities, Morgantown, 1972.

LINKS

Table of n, a(n) for n=0..16.

FORMULA

Conjecture: n*(2*n-1)*(n-1)*a(n) -12*(n-1)*(4*n^2-11*n+10)*a(n-1) +4*(38*n^3-333*n^2+715*n-435)*a(n-2) +48*(34*n^3-228*n^2+499*n-355)*a(n-3) +16*(4*n-15)*(2*n-7)*(4*n-13)*a(n-4)=0. - R. J. Mathar, Feb 20 2015

Conjecture: n*(n-1)*(2*n-1)*(5*n^2-15*n+11)*a(n) -4*(n-1)*(30*n^4-120*n^3+161*

n^2-82*n+12)*a(n-1) -4*(4*n-7)*(2*n-3)*(4*n-5)*(5*n^2-5*n+1)*a(n-2)=0. - R. J. Mathar, Feb 20 2015

MAPLE

A037964 := proc(n)

    binomial(4*n, 2*n)/2-(-1)^n*binomial(2*n, n)/2 ;

end proc: # R. J. Mathar, Feb 20 2015

CROSSREFS

Sequence in context: A214379 A192500 A192486 * A089285 A209197 A086906

Adjacent sequences:  A037961 A037962 A037963 * A037965 A037966 A037967

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified October 23 01:49 EDT 2020. Contains 337962 sequences. (Running on oeis4.)