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A256550
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Triangle read by rows, T(n,k) = EL(n,k)/(n-k+1)! and EL(n,k) the matrix-exponential of the unsigned Lah numbers scaled by exp(-1), for n>=0 and 0<=k<=n.
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1
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1, 0, 1, 0, 1, 1, 0, 2, 3, 1, 0, 5, 12, 6, 1, 0, 15, 50, 40, 10, 1, 0, 52, 225, 250, 100, 15, 1, 0, 203, 1092, 1575, 875, 210, 21, 1, 0, 877, 5684, 10192, 7350, 2450, 392, 28, 1, 0, 4140, 31572, 68208, 61152, 26460, 5880, 672, 36, 1
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OFFSET
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0,8
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LINKS
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FORMULA
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T(n+2,2) = C(n+2,2)*Bell(n) = A105479(n+2).
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EXAMPLE
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Triangle starts:
1;
0, 1;
0, 1, 1;
0, 2, 3, 1;
0, 5, 12, 6, 1;
0, 15, 50, 40, 10, 1;
0, 52, 225, 250, 100, 15, 1;
0, 203, 1092, 1575, 875, 210, 21, 1;
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PROG
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(Sage)
def T(dim) :
M = matrix(ZZ, dim)
for n in range(dim) :
M[n, n] = 1
for k in range(n) :
M[n, k] = (k*n*gamma(n)^2)/(gamma(k+1)^2*gamma(n-k+1))
E = M.exp()/exp(1)
for n in range(dim) :
for k in range(n) :
M[n, k] = E[n, k]/factorial(n-k+1)
return M
T(8) # Computes the sequence as a lower triangular matrix.
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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