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A293926
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Triangle read by rows, T(n, k) = Pochhammer(n, k) * Stirling2(2*n, k + n) for n >= 0 and 0 <= k <= n.
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2
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1, 1, 1, 7, 12, 6, 90, 195, 180, 60, 1701, 4200, 5320, 3360, 840, 42525, 114135, 176400, 157500, 75600, 15120, 1323652, 3764376, 6679134, 7484400, 5155920, 1995840, 332640, 49329280, 146386240, 287567280, 379387008, 332972640, 186666480, 60540480, 8648640
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history;
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OFFSET
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0,4
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LINKS
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FORMULA
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EXAMPLE
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Triangle starts:
[0] 1
[1] 1, 1
[2] 7, 12, 6
[3] 90, 195, 180, 60
[4] 1701, 4200, 5320, 3360, 840
[5] 42525, 114135, 176400, 157500, 75600, 15120
[6] 1323652, 3764376, 6679134, 7484400, 5155920, 1995840, 332640
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MAPLE
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seq(seq(A293926(n, k), k=0..n), n=0..7);
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MATHEMATICA
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A293617[m_, n_, k_] := Pochhammer[m, k] StirlingS2[n + m, k + m];
A293926Row[n_] := Table[A293617[n, n, k], {k, 0, n}];
Table[A293926Row[n], {n, 0, 7}] // Flatten
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PROG
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(PARI) for(n=0, 10, for(k=0, n, print1(if(n==0 && k==0, 1, ((n+k-1)!/(n-1)!)*stirling(2*n, n + k, 2)), ", "))) \\ G. C. Greubel, Nov 19 2017
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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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