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A352468
a(0) = 1; a(n) = Sum_{k=1..n} binomial(2*n,2*k)^3 * a(n-k).
2
1, 1, 217, 735751, 16225658905, 1485378967457251, 429009059656530602767, 324779065084721999818137709, 563805297587600177760431368896025, 2028620600892240327820781003315525267467, 13978450121866685445815888094629703793828769467
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OFFSET
0,3
LINKS
Table of n, a(n) for n=0..10.
FORMULA
Sum_{n>=0} a(n) * x^(2*n) / (2*n)!^3 = 1 / (1 - Sum_{n>=1} x^(2*n) / (2*n)!^3).
MATHEMATICA
a[0] = 1; a[n_] := a[n] = Sum[Binomial[2 n, 2 k]^3 a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 10}]
nmax = 20; Take[CoefficientList[Series[1/(1 - Sum[x^(2 k)/(2 k)!^3, {k, 1, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!^3, {1, -1, 2}]
CROSSREFS
Cf.
A094088
,
A336195
,
A352467
,
A352471
.
Sequence in context:
A100794
A048258
A013541
*
A167912
A038662
A121379
Adjacent sequences:
A352465
A352466
A352467
*
A352469
A352470
A352471
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy
, Mar 17 2022
STATUS
approved
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Last modified June 10 08:08 EDT 2024. Contains 373256 sequences. (Running on oeis4.)