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A306799 Expansion of e.g.f. (sec(x) + tan(x))*(BesselI(0,2*x) + BesselI(1,2*x)). 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Boustrophedon transform of A001405.

LINKS

Table of n, a(n) for n=0..24.

Index entries for sequences related to boustrophedon transform

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]

PROG

(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

CROSSREFS

Cf. A000111, A000753, A001405.

Sequence in context: A137555 A137556 A137557 * A148335 A268419 A149883

Adjacent sequences:  A306796 A306797 A306798 * A306800 A306801 A306802

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Apr 16 2019

STATUS

approved

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Last modified July 6 02:23 EDT 2022. Contains 355108 sequences. (Running on oeis4.)