A215201 - OEIS

%I #6 Feb 10 2015 16:10:44

%S 1,1,4,22,210,3690,123928,8128636,1053430654,271360277914,

%T 139369979870592,142937572590524820,292964593467450613956,

%U 1200451226250888081523716,9836015215866134276407221456,161168995194103116779231535612216,5281443249372612678523678805252800566

%N Central coefficients in Product_{k=0..n-1} (1 + 2^k*x + x^2).

%F a(n) ~ c * 2^(n*(n-1)/2), where c = 3.97351011200975226288353040315941996... . - _Vaclav Kotesovec_, Feb 10 2015

%e The coefficients in Product_{k=0..n-1} (1+2^k*x+x^2), n>=0, form the triangle:

%e 1;

%e 1, 1, 1;

%e 1, 3, 4, 3, 1;

%e 1, 7, 17, 22, 17, 7, 1;

%e 1, 15, 74, 165, 210, 165, 74, 15, 1;

%e 1, 31, 315, 1364, 2924, 3690, 2924, 1364, 315, 31, 1;

%e 1, 63, 1308, 11475, 46887, 98622, 123928, 98622, 46887, 11475, 1308, 63, 1; ...

%e in which the central terms of the rows form this sequence.

%t Flatten[{1,Table[Coefficient[Expand[Product[1 + 2^k*x + x^2,{k,0,n-1}]],x^n],{n,1,20}]}] (* _Vaclav Kotesovec_, Feb 10 2015 *)

%o (PARI) {a(n)=polcoeff(prod(k=0, n-1, 1+2^k*x+x^2+x*O(x^n)), n)}

%o for(n=0,21,print1(a(n),", "))

%K nonn

%O 0,3

%A _Paul D. Hanna_, Aug 05 2012