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.

1, 1, -2, 1, 6, -8, 8, 1, -11, 6, 12, -20, 14, 8, -12, 1, 18, -35, 20, 6, -16, 12, 24, -44, 31, 14, -38, 8, 30, -48, 32, 1, -24, 18, 48, -83, 38, 20, -28, 6, 42, -64, 44, 12, -66, 24, 48, -92, 57, 31, -36, 14, 54, -116, 72, 8, -40, 30, 60, -120, 62, 32, -88, 1, 84, -96, 68, 18, -48, 48, 72

Offset

1,3

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, Table of n, a(n) for n = 1..10000

Formula

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

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

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 +...
where
exp(A(x)) = 1 + x + x^2 + x^5 + x^7 + x^12 + x^15 + x^22 + x^26 + x^35 + x^40 + x^51 + x^57 + x^70 + x^77 +...+ x^A001318(n) +...

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)}
for(n=1, 80, print1(a(n), ", "))

Crossrefs

Cf. A111932, A001318, A000203 (sigma).

Sequence in context: A357616 A048850 A004488 * A011419 A011133 A197806

Adjacent sequences: A224973 A224974 A224975 * A224977 A224978 A224979

Keyword

sign

Author

Paul D. Hanna, Apr 21 2013

Status

approved