The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A224976

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A224976

L.g.f.: log( 1 + Sum_{n>=1} x^(n*(3*n-1)/2) + x^(n*(3*n+1)/2) ) = Sum_{n>=1} a(n)*x^n/n.
(history; published version)

#12 by Paul D. Hanna at Sun Apr 21 21:25:05 EDT 2013

STATUS

editing

approved

#11 by Paul D. Hanna at Sun Apr 21 21:24:49 EDT 2013

CROSSREFS

Cf. A111932, A001318, A000203 (sigma).

STATUS

approved

editing

#10 by Paul D. Hanna at Sun Apr 21 21:23:39 EDT 2013

STATUS

editing

approved

#9 by Paul D. Hanna at Sun Apr 21 21:23:36 EDT 2013

FORMULA

a(n) = 2*A111932(n) - sigma(n), where sigma(n) is the sum of divisors of n.

STATUS

approved

editing

#8 by Paul D. Hanna at Sun Apr 21 21:14:39 EDT 2013

STATUS

editing

approved

#7 by Paul D. Hanna at Sun Apr 21 21:14:36 EDT 2013

COMMENTS

Compare to: -log( 1 + Sum_{n>=1} (-1)^n*(x^(n*(3*n-1)/2) + x^(n*(3*n+1)/2)) ) = Sum_{n>=1} sigma(n)*x^n/n.

STATUS

approved

editing

#6 by Paul D. Hanna at Sun Apr 21 21:05:03 EDT 2013

STATUS

editing

approved

#5 by Paul D. Hanna at Sun Apr 21 21:05:00 EDT 2013

FORMULA

a(n) = 1 iff n = 2^k for k>=0.

STATUS

approved

editing

#4 by Paul D. Hanna at Sun Apr 21 20:55:54 EDT 2013

STATUS

editing

approved

#3 by Paul D. Hanna at Sun Apr 21 20:55:49 EDT 2013

NAME

L.g.f.: log( 1 + Sum_{n>=1} x^(n*(3*n-1)/2) + x^(n*(3*n+1)/2) ) = Sum_{n>=1} a(n)*x^n/n.

COMMENTS

Compare to: log( 1 + Sum_{n>=1} (-1)^n*(x^(n*(3*n-1)/2) + x^(n*(3*n+1)/2)) ) = Sum_{n>=1} sigma(n)*x^n/n.

LINKS

Paul D. Hanna, <a href="/A224976/b224976.txt">Table of n, a(n) for n = 1..10000</a>

FORMULA

L.g.f.: log(1 + Sum_{n>=1} x^A001318(n)) = Sum_{n>=1} a(n)*x^n/n, where A001318 are the generalized pentagonal numbers.

EXAMPLE

L.g.f.: A(x) = x + x^2/2 - 2*x^3/3 + x^4/4 + 6*x^5/5 - 8*x^6/6 + 8*x^7/7 + x^8/8 - 11*x^9/9 + 6*x^10/10 + 12*x^11/11 - 20*x^12/12 +...

PROG

(PARI) {a(n)=n*polcoeff(log(1+sum(k=1, n, x^(k*(3*k-1)/2) + x^(k*(3*k+1)/2))+x*O(x^n)), n)}

CROSSREFS

Cf. A001318.