Original entry on oeis.org
1, -1, 0, 0, 0, 18, -18, 70, -700, -3850, 574, -56826, 1111572, 3361512, 33911724, 58266780, -2866139848, -16171966382, -313720155122, -333432770154, 6143791050452, 221783648934584, 3761406823258348, 19173257457737964, 157733986443551784, -3667226903663595468
Offset: 0
-
SwingNumber := proc(n) option remember; n! / iquo(n, 2)!^2 end proc:
f:= n -> add((-1)^k * IncompleteBellB(n,k,seq(SwingNumber(j),j=0..n)),k=0..n):
map(f, [$0..30]); # Robert Israel, Oct 23 2023
Original entry on oeis.org
1, 1, 2, 6, 24, 102, 522, 2954, 18732, 128338, 961954, 7701386, 66224004, 603532776, 5838062076, 59440800540, 637153946792, 7149716758206, 83945137341802, 1027214990885490, 13089318802216052, 173190191614971256, 2377205362853637580, 33775960984392259580
Offset: 0
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;
A352369
Triangle read by rows. The incomplete Bell transform of the central binomial numbers.
Original entry on oeis.org
1, 0, 1, 0, 2, 1, 0, 6, 6, 1, 0, 20, 36, 12, 1, 0, 70, 220, 120, 20, 1, 0, 252, 1380, 1140, 300, 30, 1, 0, 924, 8904, 10710, 4060, 630, 42, 1, 0, 3432, 59024, 101136, 52640, 11480, 1176, 56, 1, 0, 12870, 400824, 966672, 671328, 195300, 27720, 2016, 72, 1
Offset: 0
Triangle starts:
[0] 1;
[1] 0, 1;
[2] 0, 2, 1;
[3] 0, 6, 6, 1;
[4] 0, 20, 36, 12, 1;
[5] 0, 70, 220, 120, 20, 1;
[6] 0, 252, 1380, 1140, 300, 30, 1;
[7] 0, 924, 8904, 10710, 4060, 630, 42, 1;
[8] 0, 3432, 59024, 101136, 52640, 11480, 1176, 56, 1;
[9] 0, 12870, 400824, 966672, 671328, 195300, 27720, 2016, 72, 1;
-
CentralBinomial := n -> binomial(2*n, n):
for n from 0 to 9 do
seq(IncompleteBellB(n, k, seq(CentralBinomial(j), j = 0..n)), k = 0..n) od;
Showing 1-4 of 4 results.