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A306799
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Expansion of e.g.f. (sec(x) + tan(x))*(BesselI(0,2*x) + BesselI(1,2*x)).
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0
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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
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listen;
history;
text;
internal format)
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OFFSET
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0,2
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COMMENTS
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Boustrophedon transform of A001405.
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LINKS
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Table of n, a(n) for n=0..24.
Index entries for sequences related to boustrophedon transform
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MATHEMATICA
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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]
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PROG
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(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
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CROSSREFS
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Cf. A000111, A000753, A001405.
Sequence in context: A137555 A137556 A137557 * A148335 A268419 A149883
Adjacent sequences: A306796 A306797 A306798 * A306800 A306801 A306802
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KEYWORD
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nonn
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AUTHOR
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Ilya Gutkovskiy, Apr 16 2019
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STATUS
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approved
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