A186633 - OEIS

%I #8 Nov 06 2014 07:02:36

%S 1,1,2,11,71,705,8470,127284,2231342,45505041,1048341387,27059612615,

%T 771505041184,24109351520196,818862556900962,30044548635160841,

%U 1184027932446520895,49883835880381353808,2237276988838875420087

%N G.f.: Product_{n>=1} (1 + n^n*x^n)^(1/n).

%H Vaclav Kotesovec, <a href="/A186633/b186633.txt">Table of n, a(n) for n = 0..370</a>

%F a(n) ~ n^(n-1). - _Vaclav Kotesovec_, Nov 06 2014

%e G.f.: A(x) = 1 + x + 2*x^2 + 11*x^3 + 71*x^4 + 705*x^5 +...

%e A(x) = (1 + x) *(1 + 4*x^2)^(1/2) *(1 + 27*x^3)^(1/3) *(1 + 256*x^4)^(1/4) *...

%o (PARI) {a(n)=if(n<0, 0, polcoeff(prod(k=1, n, (1+k^k*x^k+x*O(x^n))^(1/k)), n))}

%Y Cf. variant: A023881.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Mar 19 2011