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A211233
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Triangle read by rows: T(n,k) is the k-th generalized Eulerian number of order n and degree 3, n >= 1.
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4
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1, 2, 3, 1, 4, 10, 4, 1, 1, 7, 27, 13, -13, -27, -7, -1, 1, 12, 69, 16, -182, -376, -182, 16, 69, 12, 1, 1, 21, 176, -88, -1375, -3123, -1608, 1608, 3123, 1375, 88, -176, -21, -1, 1, 38, 456, -886, -8292, -20322, -6536, 35890, 65862, 35890, -6536, -20322, -8292, -886, 456, 38, 1
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OFFSET
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1,2
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LINKS
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FORMULA
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T(n,k) = k*T(n-1,k) - (n-k)*T(n-1,k-1) - (2*n-k)*T(n-1,k-2) - (3*n-k)*T(n-1,k-3) for n > 1.
(End)
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EXAMPLE
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Triangle begins
1, 2, 3;
1, 4, 10, 4, 1;
1, 7, 27, 13, -13, -27, -7, -1;
1, 12, 69, 16, -182, -376, -182, 16, 69, 12, 1;
1, 21, 176, -88, -1375, -3123, -1608, 1608, 3123, 1375, 88, ... ;
...
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PROG
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(PARI) T(n, r=3)={my(R=vector(n)); R[1]=[1..r]; for(n=2, n, my(u=R[n-1]); R[n]=vector(r*n-1, k, sum(j=0, r, (k - j*n)*if(k>j && k-j<=#u, u[k-j], 0)))); R}
{my(A=T(5)); for(n=1, #A, print(A[n]))} \\ Andrew Howroyd, May 18 2020
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CROSSREFS
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Row sums of even rows are A047682; row sums of odd rows are zero for n > 1.
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KEYWORD
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sign,tabf
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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