A357661
Expansion of e.g.f. cosh( (exp(2*x) - 1)/sqrt(2) ).
Original entry on oeis.org
1, 0, 2, 12, 60, 320, 2040, 15568, 133648, 1230336, 11962400, 123144384, 1349008320, 15731096576, 194349866880, 2527082917120, 34392647418112, 488243791183872, 7216792525799936, 110936087161801728, 1771199461131500544, 29324602146652307456
Offset: 0
-
With[{nn=30},CoefficientList[Series[Cosh[(Exp[2x]-1)/Sqrt[2]],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Mar 23 2025 *)
-
my(N=30, x='x+O('x^N)); apply(round, Vec(serlaplace(cosh((exp(2*x)-1)/sqrt(2)))))
-
a(n) = sum(k=0, n\2, 2^(n-k)*stirling(n, 2*k, 2));
A357662
Expansion of e.g.f. cosh( (exp(3*x) - 1)/sqrt(3) ).
Original entry on oeis.org
1, 0, 3, 27, 198, 1485, 12825, 132678, 1582497, 20603727, 284290560, 4132840239, 63571690485, 1038868740000, 18022911716439, 330305863479615, 6355242571945878, 127721845479277737, 2672729031195365949, 58142565625982730462, 1313557910179640120061
Offset: 0
-
my(N=30, x='x+O('x^N)); apply(round, Vec(serlaplace(cosh((exp(3*x)-1)/sqrt(3)))))
-
a(n) = sum(k=0, n\2, 3^(n-k)*stirling(n, 2*k, 2));
A357666
Expansion of e.g.f. sinh( (exp(4*x) - 1)/2 )/2.
Original entry on oeis.org
0, 1, 4, 20, 160, 1872, 25024, 348224, 5055488, 78571776, 1332573184, 24695206912, 493816963072, 10492449771520, 234399640633344, 5480635606908928, 134015043318054912, 3427700843478056960, 91642829715498336256, 2556218693498006929408
Offset: 0
-
my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(sinh((exp(4*x)-1)/2)/2)))
-
a(n) = sum(k=0, (n-1)\2, 4^(n-1-k)*stirling(n, 2*k+1, 2));
Showing 1-3 of 3 results.