A211897 G.f.: exp( Sum_{n>=1} (2^n + (-1)^n)^n * x^n/n ).
1, 1, 13, 127, 21079, 5748277, 12575820727, 76137769800001, 2378969789430032869, 263966921383940194614823, 128008718415112846211347561597, 240383035701447602719960666753525867, 1863847508172945183054545696402414919578641
Offset: 0
Keywords
Examples
G.f.: A(x) = 1 + x + 13*x^2 + 127*x^3 + 21079*x^4 + 5748277*x^5 +... such that log(A(x)) = x + 5^2*x^2 + 7^3*x^3 + 17^4*x^4 + 31^5*x^5 + 65^6*x^6 + 127^7*x^7 +...+ (2^n + (-1)^n)^n*x^n/n +...
Programs
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PARI
{a(n)=polcoeff(exp(sum(k=1, n, (2^k+(-1)^k)^k*x^k/k)+x*O(x^n)), n)} for(n=0, 20, print1(a(n), ", "))
Formula
a(n) == 1 (mod 6).