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%I A136506 #13 Mar 14 2021 20:40:30
%S A136506 1,4,15,120,3060,278256,90858768,105637584000,436355999662176,
%T A136506 6431591598617108352,340881559632021623909760,
%U A136506 65533747894341651530074060800,46081376018330435634530315478453248
%N A136506 a(n) = binomial(2^n + 2, n).
%H A136506 G. C. Greubel, <a href="/A136506/b136506.txt">Table of n, a(n) for n = 0..50</a>
%F A136506 G.f.: A(x) = Sum_{n>=0} (1 + 2^n*x)^2 * log(1 + 2^n*x)^n/n!.
%F A136506 a(n) ~ 2^(n^2) / n!. - _Vaclav Kotesovec_, Jul 02 2016
%p A136506 A136506:= n-> binomial(2^n+2,n); seq(A136506(n), n=0..20); # _G. C. Greubel_, Mar 14 2021
%t A136506 Table[Binomial[2^n+2,n],{n,0,20}] (* _Harvey P. Dale_, Jun 20 2011 *)
%o A136506 (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 A136506 (Sage) [binomial(2^n +2, n) for n in (0..20)] # _G. C. Greubel_, Mar 14 2021
%o A136506 (Magma) [Binomial(2^n +2, n): n in [0..20]]; // _G. C. Greubel_, Mar 14 2021
%Y A136506 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 A136506 Cf. A136507, A136555.
%K A136506 nonn
%O A136506 0,2
%A A136506 _Paul D. Hanna_, Jan 01 2008

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