A382800
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where A(n,k) = n! * k! * [x^n * y^k] 1 / (1 - log(1-x) * log(1-y))^3.
Original entry on oeis.org
1, 0, 0, 0, 3, 0, 0, 3, 3, 0, 0, 6, 27, 6, 0, 0, 18, 78, 78, 18, 0, 0, 72, 282, 588, 282, 72, 0, 0, 360, 1272, 2988, 2988, 1272, 360, 0, 0, 2160, 6936, 16344, 24612, 16344, 6936, 2160, 0, 0, 15120, 44496, 101448, 175632, 175632, 101448, 44496, 15120, 0
Offset: 0
Square array begins:
1, 0, 0, 0, 0, 0, ...
0, 3, 3, 6, 18, 72, ...
0, 3, 27, 78, 282, 1272, ...
0, 6, 78, 588, 2988, 16344, ...
0, 18, 282, 2988, 24612, 175632, ...
0, 72, 1272, 16344, 175632, 1669128, ...
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a(n, k) = sum(j=0, min(n, k), j!^2*binomial(j+2, 2)*abs(stirling(n, j, 1)*stirling(k, j, 1)));
A382804
a(n) = Sum_{k=0..n} k! * (k+1)! * Stirling1(n,k)^2.
Original entry on oeis.org
1, 2, 14, 260, 9588, 581952, 52096512, 6423520896, 1041005447424, 214260350714496, 54547409318781312, 16820040059243046144, 6175245603727007034624, 2661063379044058584861696, 1329787781176741647226481664, 762665713456216694195942866944
Offset: 0
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a(n) = sum(k=0, n, k!*(k+1)!*stirling(n, k, 1)^2);
A382801
Square array A(n,k), n >= 1, k >= 1, read by antidiagonals downwards, where A(n,k) = n! * k! * [x^n * y^k] (1/2) * (1 / (1 - log(1-x) * log(1-y))^2 - 1).
Original entry on oeis.org
1, 1, 1, 2, 7, 2, 6, 20, 20, 6, 24, 72, 130, 72, 24, 120, 324, 642, 642, 324, 120, 720, 1764, 3468, 4794, 3468, 1764, 720, 5040, 11304, 21372, 32964, 32964, 21372, 11304, 5040, 40320, 83448, 150120, 238404, 290976, 238404, 150120, 83448, 40320
Offset: 1
Square array begins:
1, 1, 2, 6, 24, 120, ...
1, 7, 20, 72, 324, 1764, ...
2, 20, 130, 642, 3468, 21372, ...
6, 72, 642, 4794, 32964, 238404, ...
24, 324, 3468, 32964, 290976, 2524080, ...
120, 1764, 21372, 238404, 2524080, 26048256, ...
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a(n, k) = sum(j=0, min(n, k), j!*(j+1)!*abs(stirling(n, j, 1)*stirling(k, j, 1)))/2;
Showing 1-3 of 3 results.