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A355610
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Square array T(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of e.g.f. (1 - x)^(-x^k/k!).
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6
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1, 1, 1, 1, 0, 2, 1, 0, 2, 6, 1, 0, 0, 3, 24, 1, 0, 0, 3, 20, 120, 1, 0, 0, 0, 6, 90, 720, 1, 0, 0, 0, 4, 20, 594, 5040, 1, 0, 0, 0, 0, 10, 180, 4200, 40320, 1, 0, 0, 0, 0, 5, 40, 1134, 34544, 362880, 1, 0, 0, 0, 0, 0, 15, 210, 7980, 316008, 3628800, 1, 0, 0, 0, 0, 0, 6, 70, 1904, 71280, 3207240, 39916800
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OFFSET
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0,6
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LINKS
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FORMULA
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T(0,k) = 1 and T(n,k) = (n-1)!/k! * Sum_{j=k+1..n} j/(j-k) * T(n-j,k)/(n-j)! for n > 0.
T(n,k) = n! * Sum_{j=0..floor(n/(k+1))} |Stirling1(n-k*j,j)|/(k!^j * (n-k*j)!).
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EXAMPLE
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Square array begins:
1, 1, 1, 1, 1, 1, 1, ...
1, 0, 0, 0, 0, 0, 0, ...
2, 2, 0, 0, 0, 0, 0, ...
6, 3, 3, 0, 0, 0, 0, ...
24, 20, 6, 4, 0, 0, 0, ...
120, 90, 20, 10, 5, 0, 0, ...
720, 594, 180, 40, 15, 6, 0, ...
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PROG
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(PARI) T(n, k) = n!*sum(j=0, n\(k+1), abs(stirling(n-k*j, j, 1))/(k!^j*(n-k*j)!));
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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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