OFFSET
0,5
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..440
FORMULA
a(n) = Sum_{k=0..n} Stirling1(n,k)*A000111(k).
a(n) ~ -2*(-1)^n * n! * exp(3*Pi*n/2) / (exp(3*Pi/2) - 1)^(n+1). - Vaclav Kotesovec, Feb 09 2019
MAPLE
a:=series(sec(log(1 + x)) + tan(log(1 + x)), x=0, 25): seq(n!*coeff(a, x, n), n=0..24); # Paolo P. Lava, Mar 26 2019
MATHEMATICA
nmax = 24; CoefficientList[Series[Sec[Log[1 + x]] + Tan[Log[1 + x]], {x, 0, nmax}], x] Range[0, nmax]!
e[n_] := e[n] = (2 I)^n If[EvenQ[n], EulerE[n, 1/2], EulerE[n, 0] I]; a[n_] := a[n] = Sum[StirlingS1[n, k] e[k], {k, 0, n}]; Table[a[n], {n, 0, 24}]
PROG
(Python)
from itertools import accumulate
from sympy.functions.combinatorial.numbers import stirling
def A306336(n): # generator of terms
if n == 0: return 1
blist, c = (0, 1), 0
for k in range(1, n+1):
c += stirling(n, k, kind=1, signed=True)*blist[-1]
blist = tuple(accumulate(reversed(blist), initial=0))
return c # Chai Wah Wu, Apr 18 2023
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Feb 08 2019
STATUS
approved