cp's OEIS Frontend

A038234 Triangle whose (n, k)-th entry is binomial(n, k)*4^(n - k)*4^k.

%I A038234 #21 Feb 07 2025 15:07:17
%S A038234 1,4,4,16,32,16,64,192,192,64,256,1024,1536,1024,256,1024,5120,10240,
%T A038234 10240,5120,1024,4096,24576,61440,81920,61440,24576,4096,16384,114688,
%U A038234 344064,573440,573440,344064,114688,16384,65536,524288
%N A038234 Triangle whose (n, k)-th entry is binomial(n, k)*4^(n - k)*4^k.
%C A038234 Also the absolute values of the coefficients of the Belyi Polynomial P_(i,i)(x). - _R. J. Mathar_, Oct 16 2008
%H A038234 I. Bauer, F. Catanese, F. Grunewald, <a href="http://dx.doi.org/10.1007/s00009-006-0069-7">Chebycheff and Belyi Polynomials, Dessins de'Enfants, Beauville Surfaces and Group Theory</a>, Med. J. Math. vol 3 no 2 (2006) 121-146. [From _R. J. Mathar_, Oct 16 2008]
%H A038234 B. N. Cyvin et al., <a href="http://match.pmf.kg.ac.rs/electronic_versions/Match34/match34_109-121.pdf">Isomer enumeration of unbranched catacondensed polygonal systems with pentagons and heptagons</a>, Match, No. 34 (Oct 1996), pp. 109-121.
%F A038234 G.f.: 1/(1 - 4*x - 4*x*y). - _Ilya Gutkovskiy_, Apr 21 2017
%F A038234 T(n, k) = 2^(2*n)*JacobiP(n - k, k, -1/2 - n, 1). - _Peter Luschny_, Feb 07 2025
%e A038234 1 ;
%e A038234 4 4 ;
%e A038234 16 32 16 ;
%e A038234 64 192 192 64 ;
%e A038234 256 1024 1536 1024 256 ;
%e A038234 1024 5120 10240 10240 5120 1024 ;
%e A038234 4096 24576 61440 81920 61440 24576 4096 ;
%e A038234 16384 114688 344064 573440 573440 344064 114688 16384 ;
%e A038234 65536 524288 1835008 3670016 4587520 3670016 1835008 524288 65536 ;
%e A038234 262144 2359296 9437184 22020096 33030144 33030144 22020096 9437184 2359296 262144 ;
%p A038234 seq(print(seq(4^n*binomial(n, k), k=0..n)), n=0..9);  # _Peter Luschny_, Feb 07 2025
%K A038234 nonn,tabl,easy
%O A038234 0,2
%A A038234 _N. J. A. Sloane_