A156142 P_n(1) + Q_n(1) (see A155100 and A104035), defining Q_{-1} = 0.

1, 2, 3, 7, 27, 137, 873, 6667, 59427, 605297, 6936273, 88315027, 1236909627, 18898578857, 312811478073, 5575974948187, 106493278764627, 2169463248814817, 46958188870266273, 1076202413702266147, 26035005959162168427, 662975982648919697177, 17726672005071080580873

Offset

-1,2

Links

Table of n, a(n) for n=-1..21.

Formula

a(n) ~ (1 + sqrt(2)) * 2^(2*n + 2) * n^(n + 1/2) / (Pi^(n + 1/2) * exp(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, -1, 21}] (* Jean-François Alcover, Feb 05 2014 *)
nmax = 20; Join[{1}, CoefficientList[Series[(Sin[x] + Cos[x] + 1)/(Cos[x] - Sin[x]), {x, 0, nmax}], x] * Range[0, nmax]!] (* Vaclav Kotesovec, Dec 08 2020 *)

Crossrefs

For P_n(1) - Q_n(1) see A007836.

For P_n(0) + Q_n(0) see A000111.

For P_n(1) * Q_n(1) see A156143.

Sequence in context: A371161 A128001 A264829 * A052877 A137075 A270347

Adjacent sequences: A156139 A156140 A156141 * A156143 A156144 A156145

Keyword

nonn

Author

N. J. A. Sloane, Nov 06 2009

Status

approved