A306832 Expansion of e.g.f. (sec(x) + tan(x))*exp(x)*BesselI(0,2*x).

1, 2, 6, 21, 78, 317, 1394, 6713, 35518, 207017, 1326886, 9314173, 71206344, 589413593, 5253411102, 50166344891, 510988365078, 5530178925273, 63371129667726, 766522745352829, 9759669811328648, 130477170753991277, 1827415614960825342, 26757484944450577839, 408824255195817028276

Offset: 0

Author

Ilya Gutkovskiy, Apr 16 2019

Keywords

• nonn

Comments

Boustrophedon transform of central trinomial coefficients (A002426).

Links

• Index entries for sequences related to boustrophedon transform

Crossrefs

Cf. A000111, A002426, A306822.

Programs

Mathematica

nmax = 24; CoefficientList[Series[(Sec[x] + Tan[x]) Exp[x] BesselI[0, 2 x], {x, 0, nmax}], x] Range[0, nmax]!
t[n_, 0] := 3^n Hypergeometric2F1[ 1/2, -n, 1, 4/3]; 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 count, accumulate, islice
def A306832_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
A306832_list = list(islice(A306832_gen(),40)) # Chai Wah Wu, Jun 12 2022