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

Author

Gary W. Adamson, Dec 13 2009

Keywords

• nonn

Comments

A006498 = analogous sequence using the Fibonacci numbers.

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

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

Examples

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

Crossrefs

Cf. A000041, A171645, A006498, A010551.

Programs

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

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, ...).

Extensions

Corrected by R. J. Mathar, Jul 21 2015