A298244 a(n) = n! * [x^n] (sec(x) + tan(x))^n.

1, 1, 4, 30, 320, 4400, 74016, 1472240, 33800192, 879646464, 25589632000, 822867814912, 28982612385792, 1109640105852928, 45884917741981696, 2038015221365667840, 96765606087737999360, 4890992991269273403392, 262201755871367895711744, 14859866059895961631981568, 887693530413229611155456000

Offset: 0

Author

Ilya Gutkovskiy, Jan 15 2018

Keywords

• nonn

Links

• N. J. A. Sloane, Transforms
• Index entries for sequences related to boustrophedon transform

Crossrefs

Cf. A000111, A001250, A217066, A292758, A292976, A296793.

Main diagonal of A322267.

Programs

Mathematica

Table[n! SeriesCoefficient[(Sec[x] + Tan[x])^n, {x, 0, n}], {n, 0, 20}]

Formula

a(n) ~ n! * c * d^n / sqrt(n), where d = 3.063838405249746742835218125232... and c = 0.308377491585051819518915209... - Vaclav Kotesovec, Aug 17 2019