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A330527
Expansion of e.g.f. Sum_{k>=1} (sec(x^k) + tan(x^k) - 1).
2
1, 3, 8, 41, 136, 1381, 5312, 70265, 491776, 5977561, 40270592, 1021246445, 6249389056, 135671657941, 1919826163712, 36481192888145, 355897293438976, 12422529973051441, 121674189293944832, 4514836332133978325
OFFSET
1,2
LINKS
FORMULA
a(n) = n! * Sum_{d|n} A000111(d) / d!.
MATHEMATICA
nmax = 20; CoefficientList[Series[Sum[(Sec[x^k] + Tan[x^k] - 1), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! // Rest
Table[n! DivisorSum[n, If[EvenQ[#], Abs[EulerE[#]], Abs[(2^(# + 1) (2^(# + 1) - 1) BernoulliB[# + 1])/(# + 1)]]/#! &], {n, 1, 20}]
PROG
(Python)
from math import factorial
from itertools import accumulate
def A330527(n):
c = a = factorial(n)
blist = (0, 1)
for d in range(2, n+1):
blist = tuple(accumulate(reversed(blist), initial=0))
if n % d == 0:
c += a*blist[-1]//factorial(d)
return c # Chai Wah Wu, Apr 19 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 17 2019
STATUS
approved