A382736
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where A(n,k) = n! * k! * [x^n * y^k] 1 / (exp(x) + exp(y) - exp(x+y))^4.
Original entry on oeis.org
1, 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 4, 44, 4, 0, 0, 4, 124, 124, 4, 0, 0, 4, 284, 1084, 284, 4, 0, 0, 4, 604, 5164, 5164, 604, 4, 0, 0, 4, 1244, 19804, 48044, 19804, 1244, 4, 0, 0, 4, 2524, 68524, 313804, 313804, 68524, 2524, 4, 0, 0, 4, 5084, 224284, 1707884, 3281404, 1707884, 224284, 5084, 4, 0
Offset: 0
Square array begins:
1, 0, 0, 0, 0, 0, ...
0, 4, 4, 4, 4, 4, ...
0, 4, 44, 124, 284, 604, ...
0, 4, 124, 1084, 5164, 19804, ...
0, 4, 284, 5164, 48044, 313804, ...
0, 4, 604, 19804, 313804, 3281404, ...
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a(n, k) = sum(j=0, min(n, k), j!^2*binomial(j+3, 3)*stirling(n, j, 2)*stirling(k, j, 2));
A382740
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 / (exp(x) + exp(y) - exp(x+y))^2 - 1).
Original entry on oeis.org
1, 1, 1, 1, 7, 1, 1, 19, 19, 1, 1, 43, 127, 43, 1, 1, 91, 559, 559, 91, 1, 1, 187, 2071, 4327, 2071, 187, 1, 1, 379, 7039, 25831, 25831, 7039, 379, 1, 1, 763, 22807, 133783, 233551, 133783, 22807, 763, 1, 1, 1531, 71839, 636679, 1748791, 1748791, 636679, 71839, 1531, 1
Offset: 1
Square array begins:
1, 1, 1, 1, 1, 1, ...
1, 7, 19, 43, 91, 187, ...
1, 19, 127, 559, 2071, 7039, ...
1, 43, 559, 4327, 25831, 133783, ...
1, 91, 2071, 25831, 233551, 1748791, ...
1, 187, 7039, 133783, 1748791, 18207367, ...
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a(n, k) = sum(j=0, min(n, k), j!*(j+1)!*stirling(n, j, 2)*stirling(k, j, 2))/2;
A382741
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 / (exp(x) + exp(y) - exp(x+y))^3 - 1).
Original entry on oeis.org
1, 1, 1, 1, 9, 1, 1, 25, 25, 1, 1, 57, 193, 57, 1, 1, 121, 889, 889, 121, 1, 1, 249, 3361, 7593, 3361, 249, 1, 1, 505, 11545, 47641, 47641, 11545, 505, 1, 1, 1017, 37633, 253737, 465601, 253737, 37633, 1017, 1, 1, 2041, 118969, 1228249, 3657721, 3657721, 1228249, 118969, 2041, 1
Offset: 1
Square array begins:
1, 1, 1, 1, 1, 1, ...
1, 9, 25, 57, 121, 249, ...
1, 25, 193, 889, 3361, 11545, ...
1, 57, 889, 7593, 47641, 253737, ...
1, 121, 3361, 47641, 465601, 3657721, ...
1, 249, 11545, 253737, 3657721, 40666089, ...
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a(n, k) = sum(j=0, min(n, k), j!^2*binomial(j+2, 2)*stirling(n, j, 2)*stirling(k, j, 2))/3;
Showing 1-3 of 3 results.