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A182016
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Central coefficients of triangle A182013.
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1
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1, 3, 15, 85, 531, 3545, 24833, 180251, 1344163, 10237001, 79287469, 622596063, 4945078477, 39658283943, 320689293119, 2611817435525, 21405148148051, 176396318594937, 1460795339822349, 12150467810552223, 101463416752305385, 850306144532133787
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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(M(i),i=n..2*n), where the M(n)'s are the Motzkin numbers.
Recurrence: a(n+1) = a(n) + M(2n+2) + M(2n+1) - M(n).
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MATHEMATICA
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M[n_]:=If[n==0, 1, Coefficient[(1+x+x^2)^(n+1), x^n]/(n+1)]; Table[Sum[M[i], {i, n, 2n}], {n, 0, 40}]
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PROG
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(Maxima) M(n):=coeff(expand((1+x+x^2)^(n+1)), x^n)/(n+1);
makelist(sum(M(i), i, n, 2*n), n, 0, 20);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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