OFFSET
0,3
FORMULA
a(n) = Sum_{k=0..n} binomial(n,k) * A337445(k).
a(n) ~ n! * exp(1)*(1 - sin(1))/cos(1). - Vaclav Kotesovec, Aug 23 2021
MATHEMATICA
nmax = 22; CoefficientList[Series[Exp[x] (Sec[x] - Tan[x])/(1 - x), {x, 0, nmax}], x] Range[0, nmax]!
t[n_, 0] := n! Sum[1/k!, {k, 0, n}]; t[n_, k_] := t[n, k] = t[n, k - 1] - t[n - 1, n - k]; a[n_] := t[n, n]; Table[a[n], {n, 0, 22}]
PROG
(Python)
from itertools import count, islice, accumulate
from operator import sub
def A347071_gen(): # generator of terms
blist, m = tuple(), 1
for i in count(1):
yield (blist := tuple(accumulate(reversed(blist), func=sub, initial=m)))[-1]
m = m*i + 1
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 15 2021
STATUS
approved