A101911 Binomial transform of A101910, where A101910(n) = a(A000120(n-1)) for n>0 with A101910(0) = 1.

1, 2, 5, 12, 30, 73, 169, 377, 831, 1842, 4110, 9136, 20006, 42906, 90148, 186414, 381955, 780966, 1603330, 3319952, 6949554, 14704880, 31379910, 67272276, 144212735, 307752571, 651353609, 1363714711, 2820488954, 5761343912

Offset

0,2

Comments

Also gives the records in A101910 at positions 2^n for n>=0. A000120 is the binary 1's-counting sequence.

Links

Table of n, a(n) for n=0..29.

Formula

a(n) = 1 + Sum_{k=0, n-1} C(n, k)*a(A000120(n-k-1)) for n>0, a(0)=1. a(n) = A101910(2^n) for n>=0.

Example

Equals the binomial transform of A101910, where
A101910 = {1,1,2,2,5,2,5,5,12,2,5,5,12,5,12,12,30,...}
which has the following construction:
{1,a(0),a(1),a(1),a(2),a(1),a(2),a(2),a(3),...,a(A000120(n-1)),...}
where A000120 = {0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4,...}.

Prog

(PARI) {a(n)=if(n==0, 1, 1+sum(k=0, n-1, binomial(n, k)*a(subst(Pol(binary(n-k-1)), x, 1))))}

Crossrefs

Cf. A101910, A000120.

Sequence in context: A042789 A291253 A348619 * A052109 A157748 A046170

Adjacent sequences: A101908 A101909 A101910 * A101912 A101913 A101914

Keyword

eigen,nonn

Author

Paul D. Hanna, Dec 21 2004

Status

approved