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%I #8 Mar 14 2021 20:40:23
%S 1,3,10,84,2380,237336,82598880,99949406400,422825581068000,
%T 6318976181520699840,337559127276933693852160,
%U 65182103393445184131620004864,45946437874792132748338425828443136
%N a(n) = binomial(2^n + 1, n).
%H G. C. Greubel, <a href="/A136505/b136505.txt">Table of n, a(n) for n = 0..50</a>
%F G.f.: A(x) = Sum_{n>=0} (1 + 2^n*x) * log(1 + 2^n*x)^n/n!.
%F a(n) ~ 2^(n^2) / n!. - _Vaclav Kotesovec_, Jul 02 2016
%p A136505:= n-> binomial(2^n+1,n); seq(A136505(n), n=0..20); # _G. C. Greubel_, Mar 14 2021
%t Table[Binomial[2^n+1,n], {n,0,15}] (* _Vaclav Kotesovec_, Jul 02 2016 *)
%o (PARI) {a(n)=polcoeff(sum(i=0,n,(1+2^i*x +x*O(x^n))*log(1+2^i*x +x*O(x^n))^i/i!),n)}
%o (Sage) [binomial(2^n +1, n) for n in (0..20)] # _G. C. Greubel_, Mar 14 2021
%o (Magma) [Binomial(2^n +1, n): n in [0..20]]; // _G. C. Greubel_, Mar 14 2021
%Y Sequences of the form binomial(2^n +p*n +q, n): A136556 (0,-1), A014070 (0,0), this sequence (0,1), A136506 (0,2), A060690 (1,-1), A132683 (1,0), A132684 (1,1), A132685 (2,0), A132686 (2,1), A132687 (3,-1), A132688 (3,0), A132689 (3,1).
%Y Cf. A136507, A136555.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Jan 01 2008
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