Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #10 Aug 19 2021 11:04:05
%S 1,1,2,10,75,816,11407,194480,3871075,87700736,2220246387,62010892800,
%T 1892138207375,62591994720256,2230631475837767,85188256574494720,
%U 3470563987113896475,150234341045137637376,6886077311552162511547,333165973379285030666240,16967906593223743786978375
%N a(n) = (1/24)*n!*[x^n] (9 + sectan(4*x) + 6*sectan(2*x) + 8*sectan(x)) where sectan(x) = sec(x) + tan(x).
%C See A320956 for motivation and definitions.
%p sectan := x -> sec(x) + tan(x): # sin(Pi/4 + x/2)*csc(Pi/4 - x/2)
%p egf := 9 + sectan(4*x) + 6*sectan(2*x) + 8*sectan(x):
%p ser := series(egf, x, 22): seq((1/24)*n!*coeff(ser, x, n), n=0..20);
%t m = 20;
%t sectan[x_] := Sec[x] + Tan[x];
%t egf = 9 + sectan[4x] + 6 sectan[2x] + 8 sectan[x];
%t (1/24) CoefficientList[egf + O[x]^(m+1), x] Range[0, m]! (* _Jean-François Alcover_, Aug 19 2021 *)
%o (PARI) sectan(x) = 1/cos(x) + tan(x);
%o my(x='x+O('x^25)); Vec(serlaplace(9 + sectan(4*x) + 6*sectan(2*x) + 8*sectan(x)))/24 \\ _Michel Marcus_, Aug 19 2021
%Y Cf. A000111 (n=1), A000828 (n=2), A320957 (n=3), this sequence (n=4), A320956.
%K nonn
%O 0,3
%A _Peter Luschny_, Nov 08 2018