cp's OEIS Frontend

A260116 G.f.: Sum_{n=-oo..+oo} (x + x^n)^n.

%I A260116 #7 Jul 16 2015 22:30:51
%S A260116 1,3,1,2,3,5,1,5,1,9,10,6,1,16,1,8,23,27,1,25,1,24,36,12,1,95,26,14,
%T A260116 55,52,1,77,1,131,78,18,108,207,1,20,105,303,1,135,1,190,430,24,1,697,
%U A260116 50,236,171,315,1,307,661,606,210,30,1,1845,1,32,591,899,1288,727,1,717,300,1247,1,3256,1,38,2626,1010,1387,1652,1,3925,487,42,1,6681,3741,44,465,2379,1
%N A260116 G.f.: Sum_{n=-oo..+oo} (x + x^n)^n.
%H A260116 Paul D. Hanna, <a href="/A260116/b260116.txt">Table of n, a(n) for n = 0..1000</a>
%F A260116 G.f.: 1 + Sum_{n>=1} x^n*(1 + x^(n-1))^n + x^(n^2)/(1 + x^(n+1))^n.
%e A260116 G.f.: A(x) = 1 + 3*x + x^2 + 2*x^3 + 3*x^4 + 5*x^5 + x^6 + 5*x^7 + x^8 + 9*x^9 + 10*x^10 + 6*x^11 + x^12 + 16*x^13 + x^14 + 8*x^15 + 23*x^16 +...
%e A260116 where A(x) = 1 + P(x) + N(x) with
%e A260116 P(x) = (x+x) + (x+x^2)^2 + (x+x^3)^3 + (x+x^4)^4 + (x+x^5)^5 + (x+x^6)^6 + (x+x^7)^7 +...+ (x+x^n)^n +...
%e A260116 N(x) = 1/(x+1/x) + 1/(x+1/x^2)^2 + 1/(x+1/x^3)^3 + 1/(x+1/x^4)^4 + 1/(x+1/x^5)^5 +...+ 1/(x+1/x^n)^n +...
%e A260116 Explicitly,
%e A260116 P(x) = 2*x + x^2 + 3*x^3 + 2*x^4 + 4*x^5 + x^6 + 8*x^7 + x^8 + 7*x^9 + 7*x^10 + 7*x^11 + x^12 + 22*x^13 + x^14 + 9*x^15 + 17*x^16 +...
%e A260116 N(x) = x - x^3 + x^4 + x^5 - 3*x^7 + 2*x^9 + 3*x^10 - x^11 - 6*x^13 - x^15 + 6*x^16 + 7*x^17 - 7*x^19 - 13*x^21 + 7*x^22 - x^23 +...
%o A260116 (PARI) {a(n) = local(A=1); A = sum(k=-n,n,(x+x^k)^k +x*O(x^n)); polcoeff(A,n)}
%o A260116 for(n=0,100,print1(a(n),", "))
%o A260116 (PARI) {a(n) = local(A=1); A = 1 + sum(k=1,n,x^k*(1+x^(k-1))^k + x^(k^2)/(1+x^(k+1))^k +x*O(x^n)); polcoeff(A,n)}
%o A260116 for(n=0,100,print1(a(n),", "))
%K A260116 nonn
%O A260116 0,2
%A A260116 _Paul D. Hanna_, Jul 16 2015