A381275
Expansion of e.g.f. exp(x * cos(2*x)).
Original entry on oeis.org
1, 1, 1, -11, -47, -39, 1681, 10893, -13215, -851471, -5515679, 34375397, 887687857, 3982645577, -85350572943, -1466457337859, -659043831871, 270733024430305, 3181606182917569, -24432689736388395, -1076204061663657839, -6834631528147762247, 221729710998069153617
Offset: 0
-
a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
a(n) = sum(k=0, n, (2*I)^(n-k)*a185951(n, k));
A381341
Expansion of e.g.f. exp( x * cosh(sqrt(2)*x) ).
Original entry on oeis.org
1, 1, 1, 7, 25, 81, 601, 3207, 18705, 156385, 1087441, 8962823, 84001897, 732712241, 7487525865, 78537490951, 831722893217, 9804469109953, 115549730623009, 1431784628480007, 18795444460125241, 248964703826005777, 3487888859183694329, 50283005924345951111
Offset: 0
-
a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
a(n) = sum(k=0, n, 2^((n-k)/2)*a185951(n, k));
A381342
Expansion of e.g.f. exp( x * cos(sqrt(2)*x) ).
Original entry on oeis.org
1, 1, 1, -5, -23, -39, 361, 2675, 3697, -90575, -741839, 52779, 48483865, 358510985, -1225182503, -43006420829, -239523048095, 2745896185953, 54532102774753, 144304368441179, -6547928921714999, -88336890555248327, 199686588300036553, 18186115601328322515
Offset: 0
-
a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
a(n) = sum(k=0, n, (-2)^((n-k)/2)*a185951(n, k));
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