A306832 - OEIS

%I #26 Jun 12 2022 12:01:39

%S 1,2,6,21,78,317,1394,6713,35518,207017,1326886,9314173,71206344,

%T 589413593,5253411102,50166344891,510988365078,5530178925273,

%U 63371129667726,766522745352829,9759669811328648,130477170753991277,1827415614960825342,26757484944450577839,408824255195817028276

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

%C Boustrophedon transform of central trinomial coefficients (A002426).

%H <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>

%t nmax = 24; CoefficientList[Series[(Sec[x] + Tan[x]) Exp[x] BesselI[0, 2 x], {x, 0, nmax}], x] Range[0, nmax]!

%t 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]

%o (Python)

%o from itertools import count, accumulate, islice

%o def A306832_gen(): # generator of terms

%o     blist, a, b = (1,), 1, 1

%o     yield from blist

%o     for i in count(2):

%o         yield (blist := tuple(accumulate(reversed(blist),initial=b)))[-1]

%o         a, b = b, (b*(2*i-1)+(3*i-3)*a)//i

%o A306832_list = list(islice(A306832_gen(),40)) # _Chai Wah Wu_, Jun 12 2022

%Y Cf. A000111, A002426, A306822.

%K nonn

%O 0,2

%A _Ilya Gutkovskiy_, Apr 16 2019