A130067 Binomial coefficients binomial(m,2^k) where m>=1 and 1<=2^k<=m.

1, 2, 1, 3, 3, 4, 6, 1, 5, 10, 5, 6, 15, 15, 7, 21, 35, 8, 28, 70, 1, 9, 36, 126, 9, 10, 45, 210, 45, 11, 55, 330, 165, 12, 66, 495, 495, 13, 78, 715, 1287, 14, 91, 1001, 3003, 15, 105, 1365, 6435, 16, 120, 1820, 12870, 1, 17, 136, 2380, 24310, 17, 18, 153, 3060, 43758

Offset

1,2

Comments

Provided m and k are given, the sequence index n is n=A001855(m)+k+1. Ordered by m as rows and k as columns the sequence forms a sort of a logarithmically distorted triangle. a(n) is odd if and only if A030308(n)=1.

Links

Table of n, a(n) for n=1..63.

Formula

a(n)=binomial(m,2^k), where m=max(j|A001855(j)<n) and k=n-1-A001855(m).

Example

a(6)=4 since n=6 gives m=4, k=0 and so binomial(4,2^0)=4.
a(20)=70 since n=20 gives m=8, k=2 and so binomial(8,2^2)=70.

Crossrefs

Cf. A130068, A065040, A001855, A030308.

Sequence in context: A083041 A318611 A366472 * A282906 A032303 A032215

Adjacent sequences: A130064 A130065 A130066 * A130068 A130069 A130070

Keyword

nonn

Author

Hieronymus Fischer, May 05 2007, Sep 10 2007

Status

approved