cp's OEIS Frontend

A309841 If n = Sum (2^e_k) then a(n) = Product ((e_k + 2)!).

%I A309841 #17 Oct 27 2023 13:09:48
%S A309841 1,2,6,12,24,48,144,288,120,240,720,1440,2880,5760,17280,34560,720,
%T A309841 1440,4320,8640,17280,34560,103680,207360,86400,172800,518400,1036800,
%U A309841 2073600,4147200,12441600,24883200,5040,10080,30240,60480,120960,241920,725760,1451520,604800
%N A309841 If n = Sum (2^e_k) then a(n) = Product ((e_k + 2)!).
%H A309841 Robert Israel, <a href="/A309841/b309841.txt">Table of n, a(n) for n = 0..10000</a>
%F A309841 G.f.: Product_{k>=0} (1 + (k + 2)! * x^(2^k)).
%F A309841 a(0) = 1; a(n) = (floor(log_2(n)) + 2)! * a(n - 2^floor(log_2(n))).
%F A309841 a(2^(k-1)-1) = A000178(k).
%e A309841 21 = 2^0 + 2^2 + 2^4 so a(21) = 2! * 4! * 6! = 34560.
%p A309841 a:= n-> (l-> mul((i+1)!^l[i], i=1..nops(l)))(convert(n, base, 2)):
%p A309841 seq(a(n), n=0..40);  # _Alois P. Heinz_, Feb 10 2020
%t A309841 nmax = 40; CoefficientList[Series[Product[(1 + (k + 2)! x^(2^k)), {k, 0, Floor[Log[2, nmax]] + 1}], {x, 0, nmax}], x]
%t A309841 a[0] = 1; a[n_] := (Floor[Log[2, n]] + 2)! a[n - 2^Floor[Log[2, n]]]; Table[a[n], {n, 0, 40}]
%o A309841 (PARI) a(n)={vecprod([(k+1)! | k<-Vec(select(b->b, Vecrev(digits(n, 2)), 1))])} \\ _Andrew Howroyd_, Aug 19 2019
%Y A309841 Cf. A000142, A000178, A019565, A029930, A058295, A059590, A121663, A283477.
%K A309841 nonn,look
%O A309841 0,2
%A A309841 _Ilya Gutkovskiy_, Aug 19 2019