A294312 Expansion of e.g.f. sec(x*exp(x)).

1, 0, 1, 6, 29, 180, 1501, 14434, 154265, 1856232, 24953401, 368767102, 5936244533, 103519338780, 1944554725205, 39134556793050, 840024295910833, 19157944025344464, 462629389438242673, 11792248121970820598, 316398168231432879565, 8913743651504295251844

Offset: 0

Author

Ilya Gutkovskiy, Dec 27 2017

Keywords

• nonn

Examples

			sec(x*exp(x)) = 1 + x^2/2! + 6*x^3/3! + 29*x^4/4! + 180*x^5/5! + 1501*x^6/6! + ...
		

Crossrefs

Cf. A000364, A009007, A009017, A009121, A009300, A009448, A009565, A009635, A009768, A139134, A191719, A216401, A217502, A294313, A297009, A297010.

Programs

Maple

a:=series(sec(x*exp(x)),x=0,22): seq(n!*coeff(a,x,n),n=0..21); # Paolo P. Lava, Mar 27 2019

Mathematica

nmax = 21; CoefficientList[Series[Sec[x Exp[x]], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 21; CoefficientList[Series[1/Cos[x Exp[x]], {x, 0, nmax}], x] Range[0, nmax]!