login
G.f.: Sum_{n>=1} ( (1+x)^n + 2^n*x^n )^n / 2^n.
0

%I #7 Jan 10 2019 23:17:14

%S 1,7,74,1495,43240,1615922,73898278,3995605174,249332639378,

%T 17635891283696,1394325697856104,121850733104648549,

%U 11663364820496833946,1213527023075715931420,136368036713803151862672,16459661773011647036358779,2123742016843422567243589246,291703805646180153151632977150,42495460119330209130801042623616,6544578588779477399529020939623304

%N G.f.: Sum_{n>=1} ( (1+x)^n + 2^n*x^n )^n / 2^n.

%e G.f.: A(x) = 1 + 7*x + 74*x^2 + 1495*x^3 + 43240*x^4 + 1615922*x^5 + 73898278*x^6 + 3995605174*x^7 + 249332639378*x^8 + 17635891283696*x^9 + ...

%e such that

%e A(x) = ((1+x) + 2*x)/2 + ((1+x)^2 + 2^2*x^2)^2/2^2 + ((1+x)^3 + 2^3*x^3)^3/2^3 + ((1+x)^4 + 2^4*x^4)^4/2^4 + ((1+x)^5 + 2^5*x^5)^5/2^5 + ((1+x)^6 + 2^6*x^6)^6/2^6 + ...

%o (PARI) \p120

%o {N = 25; Vec( round( sum(n=1,500, ( (1+x +x*O(x^N))^n + 2^n*x^n )^n / 2^n *1.) ))}

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jan 10 2019