OFFSET
0,3
FORMULA
Euler transform of period 5 sequence [ 1, 1, 0, 0, 0, ...]. - Michael Somos, Feb 09 2012
a(n) ~ exp(2*Pi*sqrt(n/15)) * Gamma(1/5) * Gamma(2/5) / (4 * 3^(1/20) * 5^(9/20) * Pi^(7/5) * n^(11/20)). - Vaclav Kotesovec, Aug 27 2015
EXAMPLE
1 + x + 2*x^2 + 2*x^3 + 3*x^4 + 3*x^5 + 5*x^6 + 6*x^7 + 8*x^8 + 9*x^9 + ...
MATHEMATICA
nmax = 100; CoefficientList[Series[Product[1/((1 - x^(5k+1))*(1 - x^(5k+2))), {k, 0, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 27 2015 *)
PROG
(PARI) {a(n) = if( n<0, 0, polcoeff( 1 / prod( k=1, (n+4)\5, (1 - x^(5*k - 4)) * (1 - x^(5*k - 3)), 1 + x * O(x^n)), n))} /* Michael Somos, Feb 09 2012 */
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved