A382806
a(n) = Sum_{k=0..n} (k!)^2 * binomial(k+2,2) * Stirling1(n,k)^2.
Original entry on oeis.org
1, 3, 27, 588, 24612, 1669128, 165049224, 22269896064, 3918921022656, 870149951146944, 237662482188210624, 78249086559726140160, 30547324837444471084800, 13946361918619108837939200, 7359961832428044552536217600, 4444946383758589481684168540160
Offset: 0
-
a(n) = sum(k=0, n, k!^2*binomial(k+2, 2)*stirling(n, k, 1)^2);
A382799
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))^2.
Original entry on oeis.org
1, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 4, 14, 4, 0, 0, 12, 40, 40, 12, 0, 0, 48, 144, 260, 144, 48, 0, 0, 240, 648, 1284, 1284, 648, 240, 0, 0, 1440, 3528, 6936, 9588, 6936, 3528, 1440, 0, 0, 10080, 22608, 42744, 65928, 65928, 42744, 22608, 10080, 0, 0, 80640, 166896, 300240, 476808, 581952, 476808, 300240, 166896, 80640, 0
Offset: 0
Square array begins:
1, 0, 0, 0, 0, 0, ...
0, 2, 2, 4, 12, 48, ...
0, 2, 14, 40, 144, 648, ...
0, 4, 40, 260, 1284, 6936, ...
0, 12, 144, 1284, 9588, 65928, ...
0, 48, 648, 6936, 65928, 581952, ...
-
a(n, k) = sum(j=0, min(n, k), j!*(j+1)!*abs(stirling(n, j, 1)*stirling(k, j, 1)));
A382825
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-x) * (1-y) * (1 - log(1-x) * log(1-y))^3 ).
Original entry on oeis.org
1, 1, 1, 2, 4, 2, 6, 11, 11, 6, 24, 39, 55, 39, 24, 120, 174, 255, 255, 174, 120, 720, 942, 1338, 1623, 1338, 942, 720, 5040, 6012, 8106, 10434, 10434, 8106, 6012, 5040, 40320, 44244, 56292, 72762, 82116, 72762, 56292, 44244, 40320, 362880, 369072, 442860, 560988, 668580, 668580, 560988, 442860, 369072, 362880
Offset: 0
Square array begins:
1, 1, 2, 6, 24, 120, ...
1, 4, 11, 39, 174, 942, ...
2, 11, 55, 255, 1338, 8106, ...
6, 39, 255, 1623, 10434, 72762, ...
24, 174, 1338, 10434, 82116, 668580, ...
120, 942, 8106, 72762, 668580, 6302028, ...
-
a(n, k) = sum(j=0, min(n, k), j!^2*binomial(j+2, 2)*abs(stirling(n+1, j+1, 1)*stirling(k+1, j+1, 1)));
A382802
Square array A(n,k), n >= 1, k >= 1, read by antidiagonals downwards, where A(n,k) = n! * k! * [x^n * y^k] (1/3) * (1 / (1 - log(1-x) * log(1-y))^3 - 1).
Original entry on oeis.org
1, 1, 1, 2, 9, 2, 6, 26, 26, 6, 24, 94, 196, 94, 24, 120, 424, 996, 996, 424, 120, 720, 2312, 5448, 8204, 5448, 2312, 720, 5040, 14832, 33816, 58544, 58544, 33816, 14832, 5040, 40320, 109584, 238656, 431632, 556376, 431632, 238656, 109584, 40320
Offset: 1
Square array begins:
1, 1, 2, 6, 24, 120, ...
1, 9, 26, 94, 424, 2312, ...
2, 26, 196, 996, 5448, 33816, ...
6, 94, 996, 8204, 58544, 431632, ...
24, 424, 5448, 58544, 556376, 5017480, ...
120, 2312, 33816, 431632, 5017480, 55016408, ...
-
a(n, k) = sum(j=0, min(n, k), j!^2*binomial(j+2, 2)*abs(stirling(n, j, 1)*stirling(k, j, 1)))/3;
Showing 1-4 of 4 results.