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A352436
a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/3)} binomial(n,3*k+1) * a(k) * a(n-3*k-1).
2
1, 1, 2, 6, 25, 130, 810, 5882, 48822, 455922, 4730766, 53996052, 672326226, 9069015409, 131742237040, 2050468853310, 34041605882650, 600476252401332, 11215153375288308, 221103539006813514, 4588413676426217916, 99981290070561391848, 2282329233032693093114
OFFSET
0,3
FORMULA
E.g.f.: 1 / (1 - Sum_{n>=0} a(n) * x^(3*n+1) / (3*n+1)!).
MATHEMATICA
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, 3 k + 1] a[k] a[n - 3 k - 1], {k, 0, Floor[(n - 1)/3]}]; Table[a[n], {n, 0, 22}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Mar 16 2022
STATUS
approved