A351882 Expansion of e.g.f. 1 / (1 - x)^sec(x).

1, 1, 2, 9, 42, 255, 1785, 14406, 131236, 1328037, 14809965, 180014054, 2371072374, 33607312219, 510183508471, 8255546409722, 141855645636152, 2579236008913689, 49471832899923129, 998261936044450726, 21138674688880283370, 468687157358947546415, 10858634384569444410179

Offset: 0

Author

Ilya Gutkovskiy, Feb 23 2022

Keywords

• nonn

Crossrefs

Cf. A009196, A009429, A351880, A351883.

Programs

Mathematica

nmax = 22; CoefficientList[Series[1/(1 - x)^Sec[x], {x, 0, nmax}], x] Range[0, nmax]!

PARI

my(x='x+O('x^30)); Vec(serlaplace(1/(1-x)^(1/cos(x)))) \\ Michel Marcus, Feb 23 2022

Formula

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1) * |A009429(k)| * a(n-k).

a(n) ~ n! / (Gamma(1/cos(1)) * n^(1 - 1/cos(1))) * (1 + (1 - 1/cos(1)) * sin(1) * log(n) / (n*cos(1)^2)). - Vaclav Kotesovec, Feb 24 2022