A156143 P_n(1)*Q_n(1) (see A155100 and A104035), defining Q_{-1} = 0.

1, 2, 12, 176, 4560, 184832, 10786752, 856856576, 88901310720, 11673832128512, 1892490366446592, 371226769045323776, 86660664498577428480, 23742637220974655700992, 7544062284452303484076032, 2751743952477326731196235776, 1142005572999693488899887267840, 535040063912570172630126949302272

Offset

-1,2

Links

Table of n, a(n) for n=-1..16.

Formula

a(n) ~ 2^(4*n + 17/2) * n^(2*n+3) / (Pi^(2*n+3) * exp(2*n)). - Vaclav Kotesovec, Dec 08 2020

Mathematica

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 *)

Crossrefs

Sequence in context: A059522 A271857 A113149 * A007129 A125861 A334175

Adjacent sequences: A156140 A156141 A156142 * A156144 A156145 A156146

Keyword

nonn

Author

N. J. A. Sloane, Nov 06 2009

Status

approved