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%I #13 Mar 14 2021 20:40:30
%S 1,4,15,120,3060,278256,90858768,105637584000,436355999662176,
%T 6431591598617108352,340881559632021623909760,
%U 65533747894341651530074060800,46081376018330435634530315478453248
%N a(n) = binomial(2^n + 2, n).
%H G. C. Greubel, <a href="/A136506/b136506.txt">Table of n, a(n) for n = 0..50</a>
%F G.f.: A(x) = Sum_{n>=0} (1 + 2^n*x)^2 * log(1 + 2^n*x)^n/n!.
%F a(n) ~ 2^(n^2) / n!. - _Vaclav Kotesovec_, Jul 02 2016
%p A136506:= n-> binomial(2^n+2,n); seq(A136506(n), n=0..20); # _G. C. Greubel_, Mar 14 2021
%t Table[Binomial[2^n+2,n],{n,0,20}] (* _Harvey P. Dale_, Jun 20 2011 *)
%o (PARI) {a(n)=polcoeff(sum(i=0,n,(1+2^i*x +x*O(x^n))^2*log(1+2^i*x +x*O(x^n))^i/i!),n)}
%o (Sage) [binomial(2^n +2, n) for n in (0..20)] # _G. C. Greubel_, Mar 14 2021
%o (Magma) [Binomial(2^n +2, 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), A136505 (0,1), this sequence (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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