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 A309841 If n = Sum (2^e_k) then a(n) = Product ((e_k + 2)!). 0

%I

%S 1,2,6,12,24,48,144,288,120,240,720,1440,2880,5760,17280,34560,720,

%T 1440,4320,8640,17280,34560,103680,207360,86400,172800,518400,1036800,

%U 2073600,4147200,12441600,24883200,5040,10080,30240,60480,120960,241920,725760,1451520,604800

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

%F G.f.: Product_{k>=0} (1 + (k + 2)! * x^(2^k)).

%F a(0) = 1; a(n) = (floor(log_2(n)) + 2)! * a(n - 2^floor(log_2(n))).

%F a(2^(k-1)-1) = A000178(k).

%e 21 = 2^0 + 2^2 + 2^4 so a(21) = 2! * 4! * 6! = 34560.

%p a:= n-> (l-> mul((i+1)!^l[i], i=1..nops(l)))(convert(n, base, 2)):

%p seq(a(n), n=0..40); # _Alois P. Heinz_, Feb 10 2020

%t nmax = 40; CoefficientList[Series[Product[(1 + (k + 2)! x^(2^k)), {k, 0, Floor[Log[2, nmax]] + 1}], {x, 0, nmax}], x]

%t a[0] = 1; a[n_] := (Floor[Log[2, n]] + 2)! a[n - 2^Floor[Log[2, n]]]; Table[a[n], {n, 0, 40}]

%o (PARI) a(n)={vecprod([(k+1)! | k<-Vec(select(b->b, Vecrev(digits(n, 2)), 1))])} \\ _Andrew Howroyd_, Aug 19 2019

%Y Cf. A000142, A000178, A019565, A029930, A058295, A059590, A121663, A283477.

%K nonn

%O 0,2

%A _Ilya Gutkovskiy_, Aug 19 2019

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Last modified April 4 05:34 EDT 2020. Contains 333212 sequences. (Running on oeis4.)