A351527
Expansion of e.g.f. (log(1 + log(1 + log(1 + log(1 + log(1+ x))))))^2 / 2.
Original entry on oeis.org
1, -15, 235, -4200, 86020, -2001055, 52305780, -1520815230, 48747603100, -1709228504170, 65115320810260, -2679459929923699, 118482699493123571, -5604477255138004835, 282449438671531808676, -15111729578894643263239
Offset: 2
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my(N=20, x='x+O('x^N)); Vec(serlaplace(log(1+log(1+log(1+log(1+log(1+x)))))^2/2))
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T(n, k) = if(k==0, n==1, sum(j=0, n, abs(stirling(n, j, 1))*T(j, k-1)));
a(n) = (-1)^n*sum(k=1, n-1, binomial(n-1, k)*T(k, 5)*T(n-k, 5));
A081406
a(n) = (n+1)*a(n-3), a(0)=a(1)=a(2)=1 for n>1.
Original entry on oeis.org
1, 1, 1, 4, 5, 6, 28, 40, 54, 280, 440, 648, 3640, 6160, 9720, 58240, 104720, 174960, 1106560, 2094400, 3674160, 24344320, 48171200, 88179840, 608608000, 1252451200, 2380855680, 17041024000, 36321084800, 71425670400, 528271744000, 1162274713600
Offset: 0
a(3n+2)=A034001[n]; while other subsequences are near(but not equal) to A001669, A000359.
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a:= function(k)
if k<3 then return 1;
elif k<6 then return k+1;
else return (k+1)*a(k-3);
fi;
end;
List([0..35], n-> a(n) ); # G. C. Greubel, Aug 24 2019
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a:= func< n | n le 2 select 1 else n in [3..5] select n+1 else (n+1)*Self(n-2) >;
[a(n): n in [0..35]]; // G. C. Greubel, Aug 24 2019
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f[n_]:= (n+1)*f[n-3]; f[0]=1; f[1]=1; f[2]=1; Table[f[n], {n, 30}]
RecurrenceTable[{a[0]==a[1]==a[2]==1,a[n]==(n+1)a[n-3]},a,{n,30}] (* Harvey P. Dale, Mar 06 2019 *)
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a(n) = if(n<3, 1, (n+1)*a(n-3) );
vector(35, n, a(n-1)) \\ G. C. Greubel, Aug 24 2019
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def a(n):
if n<3: return 1
elif 3<= n <= 5: return n+1
else: return (n+1)*a(n-3)
[a(n) for n in (0..35)] # G. C. Greubel, Aug 24 2019