OFFSET
0,2
COMMENTS
Boustrophedon transform of Motzkin numbers (A001006).
MATHEMATICA
nmax = 24; CoefficientList[Series[(Sec[x] + Tan[x]) Exp[x] BesselI[1, 2 x]/x, {x, 0, nmax}], x] Range[0, nmax]!
t[n_, 0] := Hypergeometric2F1[(1 - n)/2, -n/2, 2, 4]; t[n_, k_] := t[n, k] = t[n, k - 1] + t[n - 1, n - k]; a[n_] := t[n, n]; Array[a, 25, 0]
PROG
(Python)
from itertools import accumulate, count, islice
def A306836_gen(): # generator of terms
blist, a, b = (1, ), 1, 1
yield from blist
for i in count(2):
yield (blist := tuple(accumulate(reversed(blist), initial=b)))[-1]
a, b = b, (b*(2*i+1)+(3*i-3)*a)//(i+2)
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 16 2019
STATUS
approved