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A202946 a(n+1) = 6*A060544(n)*a(n). 3
3, 18, 1080, 181440, 59875200, 32691859200, 26676557107200, 30411275102208000, 46164315605151744000, 90020415430045900800000, 219289731987591814348800000, 652606242395073239502028800000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Sums of coefficients from (3n+1)th moments of binomial(m,k)*binomial(2m,k): see Maple code below.

LINKS

Table of n, a(n) for n=1..12.

Eric W. Weisstein, MathWorld: Binomial Sums

Index to divisibility sequences

FORMULA

a(n) = (1/18)*27^n*Gamma(n-1/3)*Gamma(n-2/3)*sqrt(3)/Pi.

EXAMPLE

The evaluation of sum(k=0..n, k^7*binomial(n,k)*binomial(2*n,k)) involves the polynomial 32*n^7+96*n^6-336*n^5-360*n^4+1020*n^3-42*n^2-455*n+63, the sum of the coefficients of which is 18 = a(2).

MAPLE

with(PolynomialTools); polyn := proc (q) options operator, arrow; 3^q*Pi*GAMMA(2*n)*(sum(k^q*binomial(n, k)*binomial(2*n, k), k = 0 .. n))/(27^n*sqrt(3)*GAMMA(n-floor((1/3)*q+1/3)+2/3)*GAMMA(n-floor((1/3)*q)+1/3)) end proc; coefl := proc (q) options operator, arrow; CoefficientList(expand(polyn(q)), n) end proc; coe := proc (j, h) options operator, arrow; coefl(j)[h] end proc; seq(sum(coe(3*r+1, k), k = 1 .. 5*r+1), r = 1 .. 8) ;

PROG

(PARI) print1(a=3); for(n=2, 10, print1(", ", a*=27*n*(n-3)+60)) \\ Charles R Greathouse IV, Dec 26 2011

CROSSREFS

Cf. A060544, A064350.

Sequence in context: A163261 A064846 A157544 * A000853 A065402 A131489

Adjacent sequences:  A202943 A202944 A202945 * A202947 A202948 A202949

KEYWORD

nonn,easy

AUTHOR

John M. Campbell, Dec 26 2011

STATUS

approved

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Last modified June 22 01:32 EDT 2021. Contains 345367 sequences. (Running on oeis4.)