The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A182818 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A182818

G.f.: exp( Sum_{n>=1} sigma(2n)*x^n/n ).
(history; published version)

#49 by Paul D. Hanna at Fri Dec 07 20:37:54 EST 2018

STATUS

editing

approved

#48 by Paul D. Hanna at Fri Dec 07 20:37:52 EST 2018

FORMULA

G.f.: A(x) = Product_{n>=1} (1 - x^(2*n))/(1 - x^n)^3 follow follows directly from the above formula by Joerg Arndt. - Paul D. Hanna, Dec 07 2018

CROSSREFS

Cf. A322185, A322186.

STATUS

approved

editing

#47 by Paul D. Hanna at Fri Dec 07 18:13:39 EST 2018

STATUS

editing

approved

#46 by Paul D. Hanna at Fri Dec 07 18:13:37 EST 2018

FORMULA

G.f.: A(x) = Product_{n>=1} (1 - x^(2*n))/(1 - x^n)^3 follow directly from the above formula by Joerg Arndt. - Paul D. Hanna, Dec 07 2018

CROSSREFS

Cf. A322185, A322186.

STATUS

approved

editing

#45 by Susanna Cuyler at Wed Jan 17 09:42:57 EST 2018

STATUS

proposed

approved

#44 by Ilya Gutkovskiy at Wed Jan 17 05:57:00 EST 2018

STATUS

editing

proposed

#43 by Ilya Gutkovskiy at Wed Jan 17 05:43:58 EST 2018

COMMENTS

Number of partitions of n where there are 2 kinds of even parts and 3 kinds of odd parts. - Ilya Gutkovskiy, Jan 17 2018

STATUS

approved

editing

#42 by Bruno Berselli at Thu Jan 26 02:45:36 EST 2017

STATUS

proposed

approved

#41 by Jon E. Schoenfield at Wed Jan 25 21:08:45 EST 2017

STATUS

editing

proposed

#40 by Jon E. Schoenfield at Wed Jan 25 21:08:43 EST 2017

FORMULA

G.f.: A(x) = E(x^2)/E(x)^3 where E(x)=prod(Product_{n>=1, } (1 - x^n). [_- _Joerg Arndt_, Dec 05 2010]

Conjecture: exp( sum(Sum_{n>=1, } sigma(s*n)*x^n/n) ) == prod( Product_{d divides |s, } eta(x^d)^(-moebius(d)*sigma(s/d)) ). [_- _Joerg Arndt_, Dec 05 2010]

EXAMPLE

log(A(x)) = 3*x + 7*x^2/2 + 12*x^3/3 + 15*x^4/4 + 18*x^5/5 + 28*x^6/6 + 24*x^7/7 + 31*x^8/8 + ... + sigma(2n)*x^n/n + ...

STATUS

proposed

editing