A296793 a(n) = n! * [x^n] exp(x)*(sec(x) + tan(x))^n.

1, 2, 9, 67, 705, 9601, 160429, 3175579, 72638209, 1884974185, 54709142101, 1755923320559, 61748847320545, 2360991253910069, 97518218630249005, 4327060674324941491, 205272207854416078849, 10367500700785078039473, 555414837143457708584101, 31458118283019682610004279

Offset: 0

Author

Ilya Gutkovskiy, Dec 20 2017

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..300
• J. Millar, N. J. A. Sloane and N. E. Young, A new operation on sequences: the Boustrophedon transform, J. Combin. Theory, 17A 44-54 1996 (Abstract, pdf, ps)
• N. J. A. Sloane, Transforms.
• Index entries for sequences related to boustrophedon transform

Crossrefs

Cf. A000111, A000667, A292756, A292759, A292976.

Main diagonal of A322268.

Programs

Mathematica

Table[n! SeriesCoefficient[Exp[x] (Sec[x] + Tan[x])^n, {x, 0, n}], {n, 0, 19}]

PARI

a(n) = Vec(serlaplace(exp(x)*(1/cos(x) + tan(x))^n))[n+1] \\ Iain Fox, Dec 20 2017

Formula

a(n) ~ c * d^n * n^n, where d = 1.12712316036287986633533456353714856005183790513784733... and c = 1.61865092826915643845148401952113086265743345... - Vaclav Kotesovec, Dec 21 2017