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%I #13 Jul 24 2013 05:02:56
%S 1,2,34,748,18326,476476,12864852,356540184,10072260198,288738125676,
%T 8373405644604,245112419778408,7230816383463036,214699624924363992,
%U 6410317372741724904,192309521182251747120,5793324325615333881990,175162864903898918549580
%N G.f.: 1/(1 - 32*x)^(1/16).
%F a(n) = (2^n/n!) * Product_{k=0..n-1} (16*k + 1).
%F a(n) ~ 32^n/(GAMMA(1/16)*n^(15/16)). - _Vaclav Kotesovec_, Jul 24 2013
%e G.f.: A(x) = 1 + 2*x + 34*x^2 + 748*x^3 + 18326*x^4 + 476476*x^5 +...
%e where
%e A(x)^16 = 1 + 32*x + 1024*x^2 + 32768*x^3 + 1048576*x^4 +...+ 32^n*x^n +...
%e Also,
%e A(x)^8 = 1 + 16*x + 384*x^2 + 10240*x^3 + 286720*x^4 +...+ 8^n*A000984(n)*x^n +...
%e A(x)^4 = 1 + 8*x + 160*x^2 + 3840*x^3 + 99840*x^4 +...+ 4^n*A004981(n)*x^n +...
%e A(x)^2 = 1 + 4*x + 72*x^2 + 1632*x^3 + 40800*x^4 +...+ 2^n*A224881(n)*x^n +...
%t CoefficientList[Series[1/(1-32*x)^(1/16), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Jul 24 2013 *)
%o (PARI) {a(n)=polcoeff(1/(1-32*x +x*O(x^n))^(1/16),n)}
%o for(n=0,30,print1(a(n),", "))
%o (PARI) {a(n)=(2^n/n!)*prod(k=0, n-1, 16*k + 1)}
%o for(n=0, 30, print1(a(n), ", "))
%Y Cf. A224881, A000984, A004981.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Jul 23 2013
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