A291665 a(n) = binomial(n, 2^floor(log_2(n))).

1, 1, 3, 1, 5, 15, 35, 1, 9, 45, 165, 495, 1287, 3003, 6435, 1, 17, 153, 969, 4845, 20349, 74613, 245157, 735471, 2042975, 5311735, 13037895, 30421755, 67863915, 145422675, 300540195, 1, 33, 561, 6545, 58905, 435897, 2760681, 15380937, 76904685, 350343565

Offset

1,3

Comments

All terms are odd. It follows from the definition and Kummer theorem on 2-adic order of binomial coefficients.

From Robert Israel, Aug 30 2017: (Start)

a(n) = 1 if n is a power of 2.

a(2^k+m) = a(2^k+m-1)*(1 + 2^k/m) if 1 <= m < 2^k. (End)

Links

Robert Israel, Table of n, a(n) for n = 1..3421

Vladimir Shevelev, On a Luschny question, arXiv:1708.08096 [math.NT], 2017.

Formula

a(n) = binomial(n, A053644(n)). - Michel Marcus, Dec 15 2018

Example

For n=11, k=8. So a(n) = binomial(11,8) = 165.

Maple

seq(binomial(n, 2^ilog2(n)), n=1..100); # Robert Israel, Aug 30 2017

Mathematica

Table[Binomial[n, 2^Floor@ Log2@ n], {n, 41}] (* Michael De Vlieger, Aug 29 2017 *)

Prog

(PARI) a(n) = binomial(n, 2^logint(n, 2)); \\ Michel Marcus, Dec 15 2018

Crossrefs

Cf. A053644.

Sequence in context: A309498 A059616 A125053 * A181836 A124740 A369121

Adjacent sequences: A291662 A291663 A291664 * A291666 A291667 A291668

Keyword

nonn,look

Author

Vladimir Shevelev, Aug 29 2017

Extensions

More precise definition from Michael De Vlieger, Aug 30 2017

Status

approved