A352280
a(0) = 1; a(n) = 3 * Sum_{k=0..floor((n-1)/2)} binomial(n-1,2*k) * a(n-2*k-1).
Original entry on oeis.org
1, 3, 9, 30, 117, 516, 2493, 13152, 75177, 460272, 3003921, 20806176, 152114013, 1169842368, 9435180357, 79553524224, 699531782481, 6400932102912, 60820145019801, 599036357936640, 6105903392066373, 64309189153428480, 698936466350352717, 7828833281592926208, 90270159223293364473
Offset: 0
-
a[0] = 1; a[n_] := a[n] = 3 Sum[Binomial[n - 1, 2 k] a[n - 2 k - 1], {k, 0, Floor[(n - 1)/2]}]; Table[a[n], {n, 0, 24}]
nmax = 24; CoefficientList[Series[Exp[3 Sinh[x]], {x, 0, nmax}], x] Range[0, nmax]!
-
my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(3*sinh(x)))) \\ Seiichi Manyama, Mar 26 2022
A352617
Expansion of e.g.f. exp( exp(x) + sinh(x) - 1 ).
Original entry on oeis.org
1, 2, 5, 16, 60, 254, 1199, 6206, 34827, 210264, 1355992, 9288954, 67279309, 513149498, 4107383185, 34398823888, 300629113292, 2735356900806, 25857446103571, 253472859754918, 2572266378189583, 26981781750668760, 292136508070103208, 3260640536587635410, 37472102225288489529
Offset: 0
-
a:= proc(n) option remember; `if`(n=0, 1, add(
a(n-k)*binomial(n-1, k-1)*(1+(k mod 2)), k=1..n))
end:
seq(a(n), n=0..24); # Alois P. Heinz, Mar 24 2022
-
nmax = 24; CoefficientList[Series[Exp[Exp[x] + Sinh[x] - 1], {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = (1/2) Sum[Binomial[n - 1, k - 1] (3 - (-1)^k) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 24}]
-
my(x='x+O('x^30)); Vec(serlaplace(exp( exp(x) + sinh(x) - 1 ))) \\ Michel Marcus, Mar 24 2022
A352639
Expansion of e.g.f. exp(2*sin(x)).
Original entry on oeis.org
1, 2, 4, 6, 0, -46, -192, -266, 1792, 14114, 34816, -171930, -2027520, -6522382, 34750464, 496296022, 1748500480, -12731696062, -186550845440, -617309234490, 7292215885824, 99199654760978, 248883934396416, -5836506132182090, -69729013345550336
Offset: 0
-
With[{m = 24}, Range[0, m]! * CoefficientList[Series[Exp[2*Sin[x]], {x, 0, m}], x]] (* Amiram Eldar, Mar 26 2022 *)
-
my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(2*sin(x))))
-
a(n) = if(n==0, 1, 2*sum(k=0, (n-1)\2, (-1)^k*binomial(n-1, 2*k)*a(n-2*k-1)));
Showing 1-3 of 3 results.