Original entry on oeis.org
1, 2, 5, 16, 63, 297, 1649, 10641, 78823, 662315, 6241889, 65294039, 751035233, 9420926879, 127958645921, 1870319380463, 29263787708393, 487891616911031, 8632986776222945, 161555987833199807, 3187606376603319017, 66128414623822131863, 1438861202348688524897, 32763278185929878499887
Offset: 0
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Table[Sum[Sum[Abs[StirlingS1[n-k,m]](m+1)^k,{m,0,n-k}],{k,0,n}],{n,0,23}]
A192563
a(n) = Sum_{k=0..n} abs(Stirling1(n+1,k+1))*Stirling2(n+1,k+1)*k!.
Original entry on oeis.org
1, 2, 13, 161, 3148, 87784, 3274640, 156359874, 9252910816, 662065322016, 56172251821992, 5562573507747288, 634574662217269824, 82482896750780978880, 12101565966159294983808, 1987899464090970683668944, 363036441677797499946379776
Offset: 0
-
Table[Sum[Abs[StirlingS1[n+1,k+1]]StirlingS2[n+1,k+1]k!,{k,0,n}],{n,0,100}]
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makelist(sum(abs(stirling1(n+1,k+1))*stirling2(n+1,k+1)*k!,k,0,n),n,0,12);
A383064
Square array A(n,k), n>=0, k>=0, read by antidiagonals downwards, where column k is the expansion of e.g.f. Sum_{j>=0} (j+1)^k * (-log(1-x))^j / j!.
Original entry on oeis.org
1, 1, 1, 1, 2, 2, 1, 4, 5, 6, 1, 8, 13, 17, 24, 1, 16, 35, 51, 74, 120, 1, 32, 97, 161, 244, 394, 720, 1, 64, 275, 531, 854, 1392, 2484, 5040, 1, 128, 793, 1817, 3148, 5248, 9260, 18108, 40320, 1, 256, 2315, 6411, 12134, 20940, 36966, 70508, 149904, 362880
Offset: 0
Square array begins:
1, 1, 1, 1, 1, 1, 1, ...
1, 2, 4, 8, 16, 32, 64, ...
2, 5, 13, 35, 97, 275, 793, ...
6, 17, 51, 161, 531, 1817, 6411, ...
24, 74, 244, 854, 3148, 12134, 48604, ...
120, 394, 1392, 5248, 20940, 87784, 384252, ...
720, 2484, 9260, 36966, 156680, 699894, 3274640, ...
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a(n, k) = sum(j=0, n, j!*abs(stirling(n+1, j+1, 1))*stirling(k+1, j+1, 2));
Showing 1-3 of 3 results.