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A347072
E.g.f.: -log(1 - x) * (sec(x) + tan(x)).
0
0, 1, 3, 8, 28, 119, 605, 3597, 24624, 191481, 1672273, 16240509, 173870156, 2036293453, 25910852669, 356057435177, 5255621683776, 82932788545297, 1393129225943169, 24819194946609589, 467369450831456492, 9274872837974110805, 193447045984755732413
OFFSET
0,3
COMMENTS
Boustrophedon transform of shifted factorial numbers.
FORMULA
a(n) = Sum_{k=0..n} binomial(n,k) * A104150(k) * A000111(n-k).
a(n) ~ (n-1)! * (1 + sin(1)) / cos(1). - Vaclav Kotesovec, Aug 23 2021
MATHEMATICA
nmax = 22; CoefficientList[Series[-Log[1 - x] (Sec[x] + Tan[x]), {x, 0, nmax}], x] Range[0, nmax]!
t[n_, 0] := If[n == 0, 0, (n - 1)!]; 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 accumulate, count, islice
def A347072_gen(): # generator of terms
blist, m = (0, ), 1
yield from blist
for i in count(1):
yield (blist := tuple(accumulate(reversed(blist), initial=m)))[-1]
m *= i
A347072_list = list(islice(A347072_gen(), 40)) # Chai Wah Wu, Jun 12 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 15 2021
STATUS
approved