A178882
Triangle T(n,k) = n!* A036040(n,k) read by rows, 1 <= k <= A000041(n).
Original entry on oeis.org
1, 2, 2, 6, 18, 6, 24, 96, 72, 144, 24, 120, 600, 1200, 1200, 1800, 1200, 120, 720, 4320, 10800, 7200, 10800, 43200, 10800, 14400, 32400, 10800, 720, 5040, 35280, 105840, 176400, 105840, 529200
Offset: 1
For row n = 4 the calculations are (1 4 3 6 1) times (24 24 24 24 24 ) yielding (24 96 72 144 24)
which sums to A137341(4) = 360.
Row n has A000041(n) entries:
1;
2,2;
6,18,6;
24,96,72,144,24;
120,600,1200,1200,1800,1200,120;
720,4320,10800,7200,10800,43200,10800,14400,32400,10800,720;
A373571
Triangle read by rows: Coefficients of the polynomials S2(n, x) * EP(n, x), where S2 denote the Stirling set polynomials and EP the Eulerian polynomials A173018.
Original entry on oeis.org
1, 0, 1, 0, 1, 2, 1, 0, 1, 7, 14, 7, 1, 0, 1, 18, 94, 145, 84, 17, 1, 0, 1, 41, 481, 1676, 2302, 1351, 351, 36, 1, 0, 1, 88, 2159, 14859, 40319, 49434, 29378, 8627, 1222, 72, 1, 0, 1, 183, 9052, 113919, 554030, 1236040, 1380913, 816404, 260968, 44577, 3851, 141, 1
Offset: 0
Triangle starts:
[0] [1]
[1] [0, 1]
[2] [0, 1, 2, 1]
[3] [0, 1, 7, 14, 7, 1]
[4] [0, 1, 18, 94, 145, 84, 17, 1]
[5] [0, 1, 41, 481, 1676, 2302, 1351, 351, 36, 1]
[6] [0, 1, 88, 2159, 14859, 40319, 49434, 29378, 8627, 1222, 72, 1]
Comments