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A010552 Multiply successively by 1 (once), 2 (twice), 3 (thrice), etc.

%I A010552 #30 Jun 19 2025 11:35:13
%S A010552 1,1,2,4,12,36,108,432,1728,6912,27648,138240,691200,3456000,17280000,
%T A010552 86400000,518400000,3110400000,18662400000,111974400000,671846400000,
%U A010552 4031078400000,28217548800000,197522841600000,1382659891200000,9678619238400000,67750334668800000
%N A010552 Multiply successively by 1 (once), 2 (twice), 3 (thrice), etc.
%H A010552 Alois P. Heinz, <a href="/A010552/b010552.txt">Table of n, a(n) for n = 0..300</a>
%F A010552 a(0)=1, a(n) = a(n-1)*floor(sqrt(2*n)+1/2) for n>0. - _Alois P. Heinz_, May 20 2013
%p A010552 a:= proc(n) option remember; `if`(n=0, 1,
%p A010552       a(n-1) * floor(sqrt(2*n)+1/2))
%p A010552     end:
%p A010552 seq(a(n), n=0..30); # _Alois P. Heinz_, May 20 2013
%t A010552 t = Table[n, {n, 9}, {n}] // Flatten; b[n_] := t[[n]]; a[0] = 1; a[n_] := a[n] = b[n] a[n-1]; Table[a[n], {n, 0, t // Length}] (* _Jean-François Alcover_, Feb 21 2016 *)
%o A010552 (PARI) lista(nn) = my(na = 1, i = 0, im = 1, list=List()); listput(list, na); while (i < nn, for (j=1, im, na *= im; listput(list, na); i++; ); im++; ); Vec(list); \\ _Michel Marcus_, May 20 2013; Jun 19 2025
%o A010552 (Python)
%o A010552 from math import isqrt, comb, prod
%o A010552 def A010552(n): return (a:=(m:=isqrt(k:=n<<1))+(k>m*(m+1)))**(n-comb(a,2))*prod(i**i for i in range(2,a)) # _Chai Wah Wu_, Jun 19 2025
%Y A010552 A002109 is a subsequence.
%Y A010552 Cf. A002024.
%K A010552 nonn,easy
%O A010552 0,3
%A A010552 _Mark R. Diamond_