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A352428
a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/3)} binomial(n,3*k+1) * a(n-3*k-1).
3
1, 1, 2, 6, 25, 130, 810, 5881, 48806, 455706, 4727881, 53955682, 671730246, 9059714665, 131588822822, 2047796305470, 33992509701721, 599526848094850, 11195864285933682, 220692569175568729, 4579248276057441926, 99767702172338210898, 2277136869014579978473, 54336724559407913237122
OFFSET
0,3
LINKS
FORMULA
E.g.f.: 1 / (1 - Sum_{k>=0} x^(3*k+1) / (3*k+1)!).
MATHEMATICA
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, 3 k + 1] a[n - 3 k - 1], {k, 0, Floor[(n - 1)/3]}]; Table[a[n], {n, 0, 23}]
nmax = 23; CoefficientList[Series[1/(1 - Sum[x^(3 k + 1)/(3 k + 1)!, {k, 0, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!
PROG
(PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(1/(1-sum(k=0, N\3, x^(3*k+1)/(3*k+1)!)))) \\ Seiichi Manyama, Mar 23 2022
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Mar 16 2022
STATUS
approved