OFFSET
0,2
REFERENCES
A. P. Prudnikov, Yu. A. Brychkov and O. I. Marichev, "Integrals and Series", Volume 1: "Elementary Functions", New York, Gordon and Breach Science Publishers, 1986-1992, p. 755, Eq. 6.2.2.2. MR0874986 (88f:00013)
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..1000
FORMULA
Euler transform of period 2 sequence [6, 0, ...]. - Michael Somos, Jul 09 2005
Expansion of q^(-1/4)(eta(q^2)/eta(q))^6 in powers of q. - Michael Somos, Jul 09 2005
Expansion of q^(-1/4)(1/2)k^(1/2)/k' in powers of q. - Michael Somos, Jul 09 2005
Given g.f. A(x), then B(x)=(x*A(x^4))^4 satisfies 0=f(B(x), B(x^2)) where f(u, v)=(4096uv+48u+1)v-u^2 . - Michael Somos, Jul 09 2005
Given g.f. A(x), then B(x)=x*A(x^4) satisfies 0=f(B(x), B(x^3)) where f(u, v)=(u^2-v^2)^2 -uv(1+8uv)^2 . - Michael Somos, Jul 09 2005
G.f.: Product_{k>0} (1+x^k)^6.
a(n) ~ exp(Pi * sqrt(2*n)) / (16 * 2^(1/4) * n^(3/4)). - Vaclav Kotesovec, Mar 05 2015
a(0) = 1, a(n) = (6/n)*Sum_{k=1..n} A000593(k)*a(n-k) for n > 0. - Seiichi Manyama, Apr 03 2017
G.f.: exp(6*Sum_{k>=1} (-1)^(k+1)*x^k/(k*(1 - x^k))). - Ilya Gutkovskiy, Feb 06 2018
MATHEMATICA
nmax=50; CoefficientList[Series[Product[(1+q^m)^6, {m, 1, nmax}], {q, 0, nmax}], q] (* Vaclav Kotesovec, Mar 05 2015 *)
PROG
(PARI) a(n)=if(n<0, 0, polcoeff( prod(k=1, n, 1+x^k, 1+x*O(x^n))^6, n)) /* Michael Somos, Jul 09 2005 */
(Magma) Coefficients(&*[(1+x^m)^6:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // G. C. Greubel, Feb 26 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved