A320957 a(n) = (1/6)*n!*[x^n] (2 + sec(3*x) + tan(3*x) + 3*sec(x) + 3*tan(x)).

1, 1, 2, 10, 70, 656, 7442, 99280, 1515190, 26038016, 497227682, 10445708800, 239394707110, 5943715352576, 158922998335922, 4552807055288320, 139123511874743830, 4517007538261262336, 155283277843358756162, 5634815061983539363840, 215234080472925069593350

Offset: 0

Author

Peter Luschny, Nov 08 2018

Keywords

• nonn

Comments

See A320956 for motivation and definitions.

Crossrefs

Cf. A000111 (n=1), A000828 (n=2), this sequence (n=3), A321394 (n=4), A320956.

Programs

Maple

egf := 2 + sec(3*x) + tan(3*x) + 3*sec(x) + 3*tan(x):
ser := series(egf, x, 22): seq((1/6)*n!*coeff(ser, x, n), n=0..20);

Mathematica

m = 20;
egf = 2 + Sec[3x] + Tan[3x] + 3 Sec[x] + 3 Tan[x];
(1/6) CoefficientList[egf + O[x]^(m+1), x] Range[0, m]! (* Jean-François Alcover, Aug 19 2021 *)

PARI

sectan(x) = 1/cos(x) + tan(x);
my(x='x+O('x^25)); Vec(serlaplace(2 + sectan(3*x) + 3*sectan(x)))/6 \\ Michel Marcus, Aug 19 2021