|
|
A306822
|
|
Expansion of e.g.f. (sec(x) + tan(x))*exp(2*x)*BesselI(0,2*x).
|
|
1
|
|
|
1, 3, 11, 46, 207, 988, 4989, 26734, 152827, 937212, 6192741, 44191654, 340575513, 2829201638, 25252605283, 241269232186, 2457951274627, 26602476272908, 304845053785469, 3687342610303174, 46948693772419597, 627657623728640182, 8790742273959180703, 128716280124796774354
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
Boustrophedon transform of central binomial coefficients (A000984).
|
|
LINKS
|
|
|
MATHEMATICA
|
nmax = 23; CoefficientList[Series[(Sec[x] + Tan[x]) Exp[2 x] BesselI[0, 2 x], {x, 0, nmax}], x] Range[0, nmax]!
t[n_, 0] := Binomial[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, 24, 0]
|
|
PROG
|
(Python)
from itertools import count, islice, accumulate
def A306822_gen(): # generator of terms
blist, m = tuple(), 1
for i in count(1):
yield (blist := tuple(accumulate(reversed(blist), initial=m)))[-1]
m = m*(4*i-2)//i
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|