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A180305 G.f.: 1/(1 + x*d/dx log(eta(x))), where eta(x) is Dedekind's eta(q) function without the q^(1/24) factor. 0
1, 1, 4, 11, 34, 96, 288, 833, 2456, 7175, 21054, 61633, 180674, 529220, 1550800, 4543446, 13312552, 39004278, 114281748, 334837511, 981059294, 2874447292, 8421986238, 24675963950, 72299290794, 211833080161, 620659794584, 1818500391218, 5328110328116, 15611082044176, 45739647180588, 134014753120706, 392656158141832 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..32.

FORMULA

a(n) = Sum_{k=0,n-1} sigma(n-k)*a(k) for n>0 with a(0) = 1.

G.f.: 1/(1 - sum(k>=1, x^k/(1-x^k)^2)). [Joerg Arndt, Mar 09 2014]

EXAMPLE

G.f.: A(x) = 1 + x + 4*x^2 + 11*x^3 + 34*x^4 + 96*x^5 + 288*x^6 +...

eta(x)^3/A(x) = 1 - 4*x + 10*x^3 - 21*x^6 + 39*x^10 - 66*x^15 + 104*x^21 +...+ A184363(n)*x^n +...

1 + x*d/dx log(eta(x)) = 1 - x - 3*x^2 - 4*x^3 - 7*x^4 - 6*x^5 - 12*x^6 - 8*x^7 - 15*x^8 +...+ -sigma(n)*x^n +...

PROG

(PARI) {a(n)=polcoeff(1/(1+x*deriv(log(eta(x+x*O(x^n))))), n)}

(PARI) {a(n)=if(n==0, 1, sum(k=0, n-1, sigma(n-k)*a(k)))}

(PARI) N=66; x='x+O('x^N); Vec(1/(1 - sum(k=1, N, x^k/(1-x^k)^2))) \\ Joerg Arndt, Mar 09 2014

CROSSREFS

Cf. A184363, A000203, A000041.

Sequence in context: A062460 A098324 A144791 * A060925 A027045 A243781

Adjacent sequences:  A180302 A180303 A180304 * A180306 A180307 A180308

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jan 18 2011

STATUS

approved

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Last modified December 3 21:14 EST 2016. Contains 278745 sequences.