A171646 a(1) = 1, then partial products of Product_{n>=1} (p(n)/p(n-1)*p(n)/p(n-1)) = 1*1*1*(2)*(2)*(3/2)*(3/2)*(5/3)*(5/3)*(7/5)*(7/5)*...*; p = partition numbers, A000041 starting (1, 2, 3, 5, ...).

1, 1, 1, 2, 4, 6, 9, 15, 25, 35, 49, 77, 121, 165, 225, 330, 484, 660, 900, 1260, 1764, 2352, 3136, 4312, 5929, 7777, 10201, 13635, 18225, 23760, 30976, 40656, 53361, 68607, 88209, 114345, 148225, 188650, 240100, 307230

Offset

1,4

Comments

A006498 = analogous sequence using the Fibonacci numbers.

A171645 = .............................Primes, analogous formula.

A010551 = .............................Factorial numbers, analogous formula.

Links

Table of n, a(n) for n=1..40.

Formula

a(1) = 1, then partial products of Product_{n>=1} (p(n)/p(n-1)*p(n)/p(n-1)) = 1*1*1*(2)*(2)*(3/2)*(3/2)*(5/3)*(5/3)*(7/5)*(7/5)*...; p = partition numbers, A000041 starting (1, 2, 3, 5, ...).

Example

a(12) = 77 = 1*1*1*2*2*(3/2)*(3/2)*(5/3)*(5/3)*(7/5)*(7/5)*(11/7).

Maple

A171646t := proc(n)
    local nh;
    nh := floor(n/2) ;
    combinat[numbpart](nh)/combinat[numbpart](nh-1) ;
end proc:
A171646 := proc(n)
    mul(A171646t(i), i=2..n) ;
end proc:
1, seq(A171646(n), n=2..40) ; # R. J. Mathar, Jul 21 2015

Crossrefs

Cf. A000041, A171645, A006498, A010551.

Sequence in context: A076922 A157679 A057602 * A074677 A006498 A179997

Adjacent sequences: A171643 A171644 A171645 * A171647 A171648 A171649

Keyword

nonn

Author

Gary W. Adamson, Dec 13 2009

Extensions

Corrected by R. J. Mathar, Jul 21 2015

Status

approved