A349780
Triangle read by rows, T(n, k) = A000262(n) - A349776(n, n - k) for n > 0 and T(0, 0) = 1.
Original entry on oeis.org
1, 0, 1, 0, 1, 3, 0, 1, 7, 13, 0, 1, 13, 49, 73, 0, 1, 21, 141, 381, 501, 0, 1, 31, 331, 1531, 3331, 4051, 0, 1, 43, 673, 4873, 17473, 32593, 37633, 0, 1, 57, 1233, 12993, 71793, 212913, 354033, 394353, 0, 1, 73, 2089, 30313, 241993, 1088713, 2782153, 4233673, 4596553
Offset: 0
[0] 1;
[1] 0, 1;
[2] 0, 1, 3;
[3] 0, 1, 7, 13;
[4] 0, 1, 13, 49, 73;
[5] 0, 1, 21, 141, 381, 501;
[6] 0, 1, 31, 331, 1531, 3331, 4051;
[7] 0, 1, 43, 673, 4873, 17473, 32593, 37633;
[8] 0, 1, 57, 1233, 12993, 71793, 212913, 354033, 394353;
[9] 0, 1, 73, 2089, 30313, 241993, 1088713, 2782153, 4233673, 4596553.
A096965
Number of sets of even number of even lists, cf. A000262.
Original entry on oeis.org
1, 1, 1, 7, 37, 241, 2101, 18271, 201097, 2270017, 29668681, 410815351, 6238931821, 101560835377, 1765092183037, 32838929702671, 644215775792401, 13441862819232001, 293976795292186897, 6788407001443004647, 163735077313046119861, 4142654439686285737201
Offset: 0
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a:= proc(n) option remember; `if`(n<4, [1$3, 7][n+1], ((2*n-3)
*a(n-1)+(n-1)*(2*n^2-8*n+7)*a(n-2) + (n-2)*(n-1)*(2*n-5)
*a(n-3)-(n-4)*(n-3)*(n-2)^2*(n-1)*a(n-4))/(n-2))
end:
seq(a(n), n=0..25); # Alois P. Heinz, Dec 01 2021
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Drop[ Range[0, 20]! CoefficientList[ Series[ Exp[(x/(1 - x^2))]Cosh[x^2/(1 - x^2)], {x, 0, 20}], x], 1] (* Robert G. Wilson v, Aug 19 2004 *)
Showing 1-2 of 2 results.