A385310
Expansion of e.g.f. 1/(1 - 2 * x * cos(x))^(1/2).
Original entry on oeis.org
1, 1, 3, 12, 69, 500, 4455, 46928, 571977, 7914384, 122585355, 2100940864, 39470867469, 806555184448, 17808628411119, 422498774818560, 10717948285126545, 289501146405400832, 8295124400250875667, 251300745071590317056, 8025654235707259740885, 269482309052945201181696
Offset: 0
-
a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
a001147(n) = prod(k=0, n-1, 2*k+1);
a(n) = sum(k=0, n, a001147(k)*I^(n-k)*a185951(n, k));
A385281
Expansion of e.g.f. 1/(1 - 2 * x * cosh(2*x))^(1/2).
Original entry on oeis.org
1, 1, 3, 27, 249, 2825, 41355, 708883, 13888497, 309267729, 7698772755, 211585744139, 6367841422569, 208299923870233, 7357493992966299, 279095125351544835, 11316313498670411745, 488403056864943302177, 22355228989851909617187, 1081663315375339026249211
Offset: 0
-
a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
a001147(n) = prod(k=0, n-1, 2*k+1);
a(n) = sum(k=0, n, a001147(k)*2^(n-k)*a185951(n, k));
A385284
Expansion of e.g.f. 1/(1 - 3 * x * cos(3*x))^(1/3).
Original entry on oeis.org
1, 1, 4, 1, -152, -3515, -54080, -671363, -2823296, 199955305, 10101514240, 323321153881, 7583054076928, 80180394219757, -4570380001660928, -409907196093564395, -20705306119297925120, -748794938843475359663, -14289862480447260852224, 610587389113316064978481
Offset: 0
-
a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
a007559(n) = prod(k=0, n-1, 3*k+1);
a(n) = sum(k=0, n, a007559(k)*(3*I)^(n-k)*a185951(n, k));
Showing 1-3 of 3 results.