A126391 a(1)=1; for n>1: a(n) = sum of all subsets of (a(1),..,a(n-1)).

1, 1, 4, 24, 240, 4320, 146880, 9694080, 1260230400, 325139443200, 167121673804800, 171466837323724800, 351507016513635840000, 1440475753672879672320000, 11803258325595576034990080000

Offset

1,3

Comments

Is connection with A006088 clear?

Apparently first differences of A028361. - Sean A. Irvine, Jun 25 2022

Links

Table of n, a(n) for n=1..15.

Formula

a(1)=1, a(2)=1; n>2: a(n)=(2^(n-2)+2)*a(n-1). a(1)=1; n>1: a(n)=A006088(n-1).

Example

n=2: subsets of (1) are ((0),(1)), sums of subsets are (0,1) and total sum is 0+1=1, hence a(2)=1;
n=3: subsets of (1,1) are ((0),(1),(1),(1,1)), sums of subsets are (0,1,1,2) and total sum is 0+1+1+2=4, hence a(3)=4;
n=4: subsets of (1,1,4) are ((0),(1),(1),(4),(1,1),(1,4),(1,4),(1,1,4)), sums of subsets are (0,1,1,4,2,5,5,6) and total sum is 0+1+1+4+2+5+5+6=24, hence a(4)=24.

Mathematica

a[1]=1; a[2]=1; a[n_]:=a[n]=(2^(n-2)+2)*a[n-1]; Table[a[i], {i, 18}]

Crossrefs

Cf. A006088.

Sequence in context: A239840 A052718 A061640 * A006088 A325963 A141013

Adjacent sequences: A126388 A126389 A126390 * A126392 A126393 A126394

Keyword

nonn

Author

Zak Seidov, Mar 23 2007

Status

approved