Original entry on oeis.org
1, 1, 3, 13, 69, 431, 3103, 25271, 228945, 2276803, 24605811, 286742831, 3580459501, 47647919385, 672666093583, 10033841676961, 157592244804465, 2598219867015235, 44845197606105859, 808362808229409743, 15184641619260934701, 296660002497701895445, 6017229226892950754271
Offset: 0
Original entry on oeis.org
1, -1, -1, -1, 5, 49, 259, 741, -3263, -76915, -782089, -5173763, -9197123, 389152919, 8099637883, 102525854939, 853355714673, 931100151549, -140777397537929, -3587404181388531, -58439969237350259, -649453301904349909, -2064509243175655605, 131896195608069986079
Offset: 0
A352363
Triangle read by rows. The incomplete Bell transform of the swinging factorials A056040.
Original entry on oeis.org
1, 0, 1, 0, 1, 1, 0, 2, 3, 1, 0, 6, 11, 6, 1, 0, 6, 50, 35, 10, 1, 0, 30, 166, 225, 85, 15, 1, 0, 20, 756, 1246, 735, 175, 21, 1, 0, 140, 2932, 7588, 5761, 1960, 322, 28, 1, 0, 70, 11556, 45296, 46116, 20181, 4536, 546, 36, 1
Offset: 0
Triangle starts:
[0] 1;
[1] 0, 1;
[2] 0, 1, 1;
[3] 0, 2, 3, 1;
[4] 0, 6, 11, 6, 1;
[5] 0, 6, 50, 35, 10, 1;
[6] 0, 30, 166, 225, 85, 15, 1;
[7] 0, 20, 756, 1246, 735, 175, 21, 1;
[8] 0, 140, 2932, 7588, 5761, 1960, 322, 28, 1;
[9] 0, 70, 11556, 45296, 46116, 20181, 4536, 546, 36, 1;
-
SwingNumber := n -> n! / iquo(n, 2)!^2:
for n from 0 to 9 do
seq(IncompleteBellB(n, k, seq(SwingNumber(j), j = 0..n)), k = 0..n) od;
A352366
Triangle read by rows. The incomplete Bell transform of the Catalan numbers.
Original entry on oeis.org
1, 0, 1, 0, 1, 1, 0, 2, 3, 1, 0, 5, 11, 6, 1, 0, 14, 45, 35, 10, 1, 0, 42, 199, 210, 85, 15, 1, 0, 132, 938, 1309, 700, 175, 21, 1, 0, 429, 4675, 8498, 5789, 1890, 322, 28, 1, 0, 1430, 24489, 57455, 48762, 19929, 4410, 546, 36, 1
Offset: 0
Triangle start:
[0] 1;
[1] 0, 1;
[2] 0, 1, 1;
[3] 0, 2, 3, 1;
[4] 0, 5, 11, 6, 1;
[5] 0, 14, 45, 35, 10, 1;
[6] 0, 42, 199, 210, 85, 15, 1;
[7] 0, 132, 938, 1309, 700, 175, 21, 1;
[8] 0, 429, 4675, 8498, 5789, 1890, 322, 28, 1;
[9] 0, 1430, 24489, 57455, 48762, 19929, 4410, 546, 36, 1;
-
CatalanNumber := n -> binomial(2*n, n)/(n + 1):
for n from 0 to 9 do
seq(IncompleteBellB(n, k, seq(CatalanNumber(j), j=0 .. n)), k = 0..n) od;
Showing 1-4 of 4 results.