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A104982
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Column 3 of triangle A104980, omitting leading zeros.
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4
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1, 4, 21, 133, 977, 8135, 75609, 775667, 8707057, 106185715, 1398451353, 19786121467, 299384925569, 4825081148819, 82531968286569, 1493412479919371, 28504390805515921, 572363196501249667, 12061937537478658809
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OFFSET
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0,2
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COMMENTS
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Equals one-half of column 0 (after initial term) in triangle A104988, which equals the matrix square of triangle A104980.
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LINKS
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FORMULA
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MATHEMATICA
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T[n_, k_]:= T[n, k]= If[k<0 || k>n, 0, If[k==n, 1, If[k==n-1, n, k*T[n, k+1] + Sum[T[j, 0]*T[n, j+k+1], {j, 0, n-k-1}]]]];
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PROG
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(PARI) {a(n) = if(n<0, 0, (matrix(n+4, n+4, m, j, if(m==j, 1, if(m==j+1, -m+1, -polcoeff((1-1/sum(i=0, m, i!*x^i))/x +O(x^m), m-j-1))))^-1)[n+4, 4])}
(Sage)
@CachedFunction
def T(n, k):
if (k<0 or k>n): return 0
elif (k==n): return 1
elif (k==n-1): return n
else: return k*T(n, k+1) + sum( T(j, 0)*T(n, j+k+1) for j in (0..n-k-1) )
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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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