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A105871
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a(n) = sum{k=0..floor(n/2), C(2*n-3*k, n)*C(n-k, k)}
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1
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1, 2, 6, 22, 85, 336, 1350, 5492, 22554, 93300, 388201, 1622868, 6811056, 28680356, 121111440, 512684484, 2174928031, 9243973062, 39354962345, 167799259130, 716414975613, 3062437147352, 13105366936465, 56139506687280
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = sum{k=0..floor(n/2), C(2*n-3*k, n)*C(n-k, k)}
Conjecture: 5*n*(n-1)*(3*n-10)*a(n) -3*(n-1)*(21*n^2-63*n-20)*a(n-1) +3*(-3*n^3+107*n^2-446*n+444)*a(n-2) +(3*n^3-259*n^2+1279*n-1575)*a(n-3) +3*(-21*n^3+210*n^2-673*n+694)*a(n-4) -3*(n-3)*(3*n^2-8*n-7)*a(n-5) -2*(n-4)*(3*n-7)*(2*n-9)*a(n-6)=0. - R. J. Mathar, Feb 20 2015
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MAPLE
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add(binomial(2*n-3*k, n)*binomial(n-k, k), k=0..floor(n/2)) ;
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MATHEMATICA
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Table[Sum[Binomial[2n-3k, n]Binomial[n-k, k], {k, 0, Floor[n/2]}], {n, 0, 30}] (* Harvey P. Dale, Jan 23 2023 *)
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PROG
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(PARI) a(n)=sum(k=0, floor(n/2), binomial(2*n-3*k, n)*binomial(n-k, k) ); /* Joerg Arndt, Mar 06 2013 */
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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