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

1, 2, 6, 12, 24, 48, 144, 288, 120, 240, 720, 1440, 2880, 5760, 17280, 34560, 720, 1440, 4320, 8640, 17280, 34560, 103680, 207360, 86400, 172800, 518400, 1036800, 2073600, 4147200, 12441600, 24883200, 5040, 10080, 30240, 60480, 120960, 241920, 725760, 1451520, 604800

Offset: 0

Author

Ilya Gutkovskiy, Aug 19 2019

Keywords

• nonn
• look

Examples

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

Links

• Robert Israel, Table of n, a(n) for n = 0..10000

Crossrefs

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

Programs

Maple

a:= n-> (l-> mul((i+1)!^l[i], i=1..nops(l)))(convert(n, base, 2)):
seq(a(n), n=0..40);  # Alois P. Heinz, Feb 10 2020

Mathematica

nmax = 40; CoefficientList[Series[Product[(1 + (k + 2)! x^(2^k)), {k, 0, Floor[Log[2, nmax]] + 1}], {x, 0, nmax}], x]
a[0] = 1; a[n_] := (Floor[Log[2, n]] + 2)! a[n - 2^Floor[Log[2, n]]]; Table[a[n], {n, 0, 40}]

PARI

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

Formula

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

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

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