A185323 E.g.f. A(x) = 1/(2-tan(x)-sec(x)).

1, 1, 3, 14, 87, 676, 6303, 68564, 852387, 11921476, 185259603, 3166825364, 59054916687, 1193026564276, 25955467164903, 605021502144164, 15043243752072987, 397412126087559076, 11116403953041202203, 328222705791221254964

Offset: 0

Author

Vladimir Kruchinin, Feb 17 2011

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..415
• Vladimir Kruchinin, D. V. Kruchinin, Composita and their properties, arXiv:1103.2582 [math.CO], 2011.

Programs

Maple

T:= proc(n, k) option remember;
      if k=n then 1
    elif k<0 or k>n then 0
    else T(n-1, k-1) +k*T(n-1, k) +k*(k+1)/2 *T(n-1, k+1)
      fi
    end:
a:= n-> add(k! * T(n, k), k=0..n):
seq(a(n), n=0..30);  # Alois P. Heinz, Feb 18 2011

Mathematica

CoefficientList[Series[1/(2-Tan[x]-Sec[x]), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Sep 25 2013 *)

PARI

x = 'x + O('x^30); Vec(serlaplace(1/(2-tan(x)-1/cos(x)))) \\ Michel Marcus, Jun 27 2017

Formula

a(n) = Sum_{k=1..n} k!*A147315(n,k), n>0. a(0)=1.

E.g.f.: 1 + x/(U(0)-x) where U(k)= 4*k+1 - x/(2 - x/(4*k+3 + x/(2 + x/U(k+1))));(continued fraction, 4-step). - Sergei N. Gladkovskii, Nov 08 2012

a(n) ~ n! * 2/(5*arctan(3/4)^(n+1)). - Vaclav Kotesovec, Sep 25 2013