OFFSET
0,2
COMMENTS
Boustrophedon transform of A000165 (double factorial of even numbers).
LINKS
FORMULA
a(n) ~ n! * (sec(1/2) + tan(1/2)) * 2^n. - Vaclav Kotesovec, Jun 07 2019
MAPLE
N:= 25: # for a(0)..a(N)
S:= series((sec(x)+tan(x))/(1-2*x), x, N+1):
seq(coeff(S, x, n)*n!, n=0..N); # Robert Israel, Jun 06 2019
MATHEMATICA
nmax = 19; CoefficientList[Series[(Sec[x] + Tan[x])/(1 - 2 x), {x, 0, nmax}], x] Range[0, nmax]!
t[n_, 0] := 2^n n!; t[n_, k_] := t[n, k] = t[n, k - 1] + t[n - 1, n - k]; a[n_] := t[n, n]; Array[a, 20, 0]
PROG
(Python)
from itertools import count, islice, accumulate
def A308521_gen(): # generator of terms
blist, m = tuple(), 1
for i in count(1):
yield (blist := tuple(accumulate(reversed(blist), initial=m)))[-1]
m *= 2*i
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jun 04 2019
STATUS
approved