A292976 a(n) = n! * [x^n] exp(n*x)*(sec(x) + tan(x)).

1, 2, 9, 65, 645, 8141, 124729, 2247853, 46584937, 1091386465, 28521016621, 822514469149, 25946988879053, 888784357214729, 32851731018695905, 1303291334592451037, 55235983848811714129, 2490726416399046168993, 119065442891277782378581, 6014589653389306889686941

Offset: 0

Author

Ilya Gutkovskiy, Sep 27 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..386
• N. J. A. Sloane, Transforms
• Index entries for sequences related to boustrophedon transform

Crossrefs

Main diagonal of A292975.

Cf. A000111.

Programs

Maple

b:= proc(u, o) option remember; `if`(u+o=0, 1,
      add(b(o-1+j, u-j), j=1..u))
    end:
A:= proc(n, k) option remember; `if`(k=0, b(n, 0),
      add(binomial(n, j)*A(j, k-1), j=0..n))
    end:
a:= n-> A(n$2):
seq(a(n), n=0..20);  # Alois P. Heinz, Sep 27 2017

Mathematica

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

Formula

a(n) = A292975(n,n).

a(n) ~ (1 + sin(1)) / cos(1) * n^n. - Vaclav Kotesovec, Oct 06 2017