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A202190
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Triangle T(n,m) = coefficient of x^n in expansion of [x*(x+1)^(x+1)]^m = sum(n>=m, T(n,m) x^n*m!/n!).
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0
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1, 2, 1, 6, 6, 1, 12, 36, 12, 1, 40, 180, 120, 20, 1, 60, 960, 1020, 300, 30, 1, 378, 4620, 8400, 3780, 630, 42, 1, -336, 24864, 65520, 44240, 10920, 1176, 56, 1, 8496, 114912, 512568, 488880, 171360, 26712, 2016, 72, 1, -51120, 679680, 3885840, 5261760
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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,m):=(n)!/(m)!*sum(k=0..n-m, k!*sum(i=k..n-m, (stirling1(i,k)*binomial(k,n-i-m))/i!)*m^k/k!).
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EXAMPLE
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1
2, 1,
6, 6, 1,
12, 36, 12, 1,
40, 180, 120, 20, 1,
60, 960, 1020, 300, 30, 1,
378, 4620, 8400, 3780, 630, 42, 1
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PROG
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(Maxima)
T(n, m):=(n)!/(m)!*sum(k!*sum((stirling1(i, k)*binomial(k, n-i-m))/i!, i, k, n-m)*m^k/k!, k, 0, n-m);
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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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