A306799 Expansion of e.g.f. (sec(x) + tan(x))*(BesselI(0,2*x) + BesselI(1,2*x)).

1, 2, 5, 14, 43, 151, 597, 2701, 13795, 79129, 503693, 3527292, 26945081, 222997659, 1987492223, 18979143358, 193319844179, 2092211006561, 23974970862885, 289995870991594, 3692342091149853, 49362977658760079, 691359846917532235, 10123067013673200297, 154669070822937580645

Offset: 0

Author

Ilya Gutkovskiy, Apr 16 2019

Keywords

• nonn

Comments

Boustrophedon transform of A001405.

Links

• Index entries for sequences related to boustrophedon transform

Crossrefs

Cf. A000111, A000753, A001405.

Programs

Mathematica

nmax = 24; CoefficientList[Series[(Sec[x] + Tan[x]) (BesselI[0, 2 x] + BesselI[1, 2 x]), {x, 0, nmax}], x] Range[0, nmax]!
t[n_, 0] := Binomial[n, Floor[n/2]]; t[n_, k_] := t[n, k] = t[n, k - 1] + t[n - 1, n - k]; a[n_] := t[n, n]; Array[a, 25, 0]

Python

from itertools import accumulate, count, islice
def A306799_gen(): # generator of terms
    blist, a  = tuple(), 1
    for i in count(1):
        yield (blist := tuple(accumulate(reversed(blist),initial=a)))[-1]
        a = 2*a*i//(i+1) if i & 1 else 2*a
A306799_list = list(islice(A306799_gen(),30)) # Chai Wah Wu, Jun 11 2022