A171646 - OEIS

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

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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