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A292976
a(n) = n! * [x^n] exp(n*x)*(sec(x) + tan(x)).
5
1, 2, 9, 65, 645, 8141, 124729, 2247853, 46584937, 1091386465, 28521016621, 822514469149, 25946988879053, 888784357214729, 32851731018695905, 1303291334592451037, 55235983848811714129, 2490726416399046168993, 119065442891277782378581, 6014589653389306889686941
OFFSET
0,2
FORMULA
a(n) = A292975(n,n).
a(n) ~ (1 + sin(1)) / cos(1) * n^n. - Vaclav Kotesovec, Oct 06 2017
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}]
CROSSREFS
Main diagonal of A292975.
Cf. A000111.
Sequence in context: A062395 A352986 A099975 * A334315 A334263 A127056
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Sep 27 2017
STATUS
approved