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A190734 Central coefficients of the Riordan matrix A121576. 0
1, 5, 51, 618, 8043, 108753, 1505652, 21181632, 301445115, 4327546335, 62550664827, 909065484726, 13271032349844, 194464001709708, 2858582670411768, 42135099729748512, 622533141544186779, 9216768941364987195, 136706015987753749593 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..18.

FORMULA

a(n) = [x^n](1-2*x-2*x^2)*(1+2*x)^(2*n)/(1-x)^(2*n+1).

a(n) = sum(i=0..n, binomial(2*n,i) * binomial(3*n-i,2*n) * (8*n^2-12*(i-1)*n+3*i^2-9*i+4) / ((2*n-i+2)*(2*n-i+1))*2^i)/2

MATHEMATICA

Sum[Binomial[2n, i]Binomial[3n-i, 2n](4-9i+3i^2-12(i-1)n+8n^2)/((2n-i+2)(2n-i+1))2^i, {i, 0, n}]/2

PROG

(Maxima) makelist(sum(binomial(2*n, i)*binomial(3*n-i, 2*n)*(4-9*i+3*i^2-12*(i-1)*n+8*n^2)/((2*n-i+2)*(2*n-i+1))*2^i, i, 0, n)/2, n, 0, 12);

CROSSREFS

Cf. A121576.

Sequence in context: A223002 A180511 A245926 * A154886 A268138 A145162

Adjacent sequences:  A190731 A190732 A190733 * A190735 A190736 A190737

KEYWORD

nonn

AUTHOR

Emanuele Munarini, May 18 2011

STATUS

approved

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Last modified October 18 01:04 EDT 2019. Contains 328135 sequences. (Running on oeis4.)