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A185323
E.g.f. A(x) = 1/(2-tan(x)-sec(x)).
1
1, 1, 3, 14, 87, 676, 6303, 68564, 852387, 11921476, 185259603, 3166825364, 59054916687, 1193026564276, 25955467164903, 605021502144164, 15043243752072987, 397412126087559076, 11116403953041202203, 328222705791221254964
OFFSET
0,3
LINKS
Vladimir Kruchinin, D. V. Kruchinin, Composita and their properties, arXiv:1103.2582 [math.CO], 2011.
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
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 *)
PROG
(PARI) x = 'x + O('x^30); Vec(serlaplace(1/(2-tan(x)-1/cos(x)))) \\ Michel Marcus, Jun 27 2017
CROSSREFS
Sequence in context: A121587 A332256 A335849 * A222714 A199548 A355294
KEYWORD
nonn
AUTHOR
Vladimir Kruchinin, Feb 17 2011
STATUS
approved