cp's OEIS Frontend

A103263 Number of partitions of n into distinct parts prime to 3 and 5.

%I A103263 #14 Sep 06 2015 10:13:29
%S A103263 1,1,1,1,1,1,1,2,2,2,2,3,3,4,5,5,5,6,7,8,9,10,11,12,14,15,17,18,20,22,
%T A103263 25,28,30,33,36,39,43,48,52,56,61,67,73,80,87,94,101,110,120,130,141,
%U A103263 152,164,177,192,207,223,240,258,278,301,324,348,373,400,429,461,496
%N A103263 Number of partitions of n into distinct parts prime to 3 and 5.
%F A103263 Expansion of q^(-1/3)(eta(q^2)*eta(q^3)*eta(q^5)*eta(q^30))/(eta(q)*eta(q^6)*eta(q^10)*eta(q^15)) in powers of q. - _Michael Somos_, Sep 22 2005.
%F A103263 G.f.: product_{k>0}((1+x^k)*(1+x^(15k)))/((1+x^(3k))*(1+x^(5k))).
%F A103263 Euler transform of period 30 sequence [1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, ...]. - _Michael Somos_, Sep 22 2005
%F A103263 Given g.f. A(x), then B(x)=x*A(x^3) satisfies 0=f(B(x), B(x^2)) where f(u, v)=u*(u-v^2)^2 +v*(v-u^2)^2 -u*v -(u*v)^3. - _Michael Somos_, Sep 22 2005
%F A103263 Given g.f. A(x), then B(x)=x*A(x^3) satisfies 0=f(B(x), B(x^2), B(x^4)) where f(u, v, w)=(v+u*w)^2 -v*(u^2+w^2). - _Michael Somos_, Sep 22 2005
%F A103263 G.f.: Product_{k>0} (1+x^k-x^(3k)-x^(4k)-x^(5k)+x^(7k)+x^(8k)). - _Michael Somos_ Sep 22 2005
%F A103263 a(n) ~ exp(2*Pi*sqrt(2*n/5)/3) / (2^(3/4) * sqrt(3) * 5^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Sep 06 2015
%e A103263 E.g. a(15)=5 because we can write 15 as 14+1=13+2=11+4=8+7=8+4+2+1.
%p A103263 series(product((1+x^k)*(1+x^(15*k))/((1+x^(3*k))*(1+x^(5*k))),k=1..100),x=0,100);
%t A103263 CoefficientList[ Series[ Product[(1 + x^k)(1 + x^(15*k))/((1 + x^(3k))*(1 + x^(5k))), {k, 100}], {x, 0, 75}], x] (* _Robert G. Wilson v_, Feb 22 2005 *)
%o A103263 (PARI) {a(n)=local(A); if (n<0, 0, A=x*O(x^n); polcoeff( eta(x^2+A)*eta(x^3+A)*eta(x^5+A)*eta(x^30+A)/ (eta(x+A)*eta(x^6+A)*eta(x^10+A)*eta(x^15+A)), n))} /* _Michael Somos_, Sep 22 2005 */
%K A103263 easy,nonn
%O A103263 0,8
%A A103263 _Noureddine Chair_, Feb 21 2005
%E A103263 More terms from _Robert G. Wilson v_, Feb 22 2005