A214936 a(0) = 1, a(n) = a(n - 1) * (length of binary representation of n).

1, 1, 2, 4, 12, 36, 108, 324, 1296, 5184, 20736, 82944, 331776, 1327104, 5308416, 21233664, 106168320, 530841600, 2654208000, 13271040000, 66355200000, 331776000000, 1658880000000, 8294400000000, 41472000000000, 207360000000000, 1036800000000000, 5184000000000000

Offset: 0

Author

Alex Ratushnyak, Jul 29 2012

Keywords

• nonn
• base
• easy

Examples

			a(4) = 12 because a(3) = 4 and 4 in binary is 100 (3 bits), and thus 4 * 3 = 12.
		

Crossrefs

Cf. A070939.

Cf. A083652: a(0)=1, for n>0: a(n)=a(n-1)+A070939(n).

Programs

Mathematica

nxt[{n_,a_}]:={n+1,a*IntegerLength[n+1,2]}; Transpose[NestList[nxt,{0,1},30]][[2]] (* Harvey P. Dale, Oct 11 2015 *)

Python

t = 1
for n in range(1,33):
    print(t, end=', ')
    t *= len(bin(n))-2

Formula

a(0) = 1, for n > 0: a(n) = a(n - 1) * (Length of binary representation of n) = a(n - 1) * A070939(n).