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P_n(1)*Q_n(1) (see A155100 and A104035), defining Q_{-1} = 0.
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%I #7 Dec 08 2020 12:07:12

%S 1,2,12,176,4560,184832,10786752,856856576,88901310720,11673832128512,

%T 1892490366446592,371226769045323776,86660664498577428480,

%U 23742637220974655700992,7544062284452303484076032,2751743952477326731196235776,1142005572999693488899887267840,535040063912570172630126949302272

%N P_n(1)*Q_n(1) (see A155100 and A104035), defining Q_{-1} = 0.

%F a(n) ~ 2^(4*n + 17/2) * n^(2*n+3) / (Pi^(2*n+3) * exp(2*n)). - _Vaclav Kotesovec_, Dec 08 2020

%t p[n_, u_] := D[Tan[x], {x, n}] /. Tan[x] -> u /. Sec[x] -> Sqrt[1+u^2] // Expand; p[-1, u_] = 1; t[n_, k_] := t[n, k] = k*t[n-1, k-1]+(k+1)*t[n-1, k+1]; t[0, 0] = 1; t[0, _] = 0; t[-1, _] = 0; q[n_, u_] := Sum[t[n, k]*u^k, {k, 0, n}]; a[n_] := p[n, 1]*q[n, 1]; Table[a[n], {n, 0, 17}] (* _Jean-François Alcover_, Feb 05 2014 *)

%K nonn

%O -1,2

%A _N. J. A. Sloane_, Nov 06 2009