A253255 - OEIS

%I #10 May 31 2015 15:05:59

%S 1,4,26,202,1731,15780,150117,1473292,14807363,151638550,1576616125,

%T 16598802248,176599380271,1895767748376,20508188211018,

%U 223348309510194,2446792909432683,26944972018189698,298111489130625351,3312016395569631402,36935315970911333184,413308467174788509668

%N G.f. satisfies: A(x) = (1 - x^3*A(x)^3)^2 / (1 - x*A(x))^4.

%C  Self-convolution of A253256.

%F G.f. A(x) satisfies:

%F (1) A(x) = exp( Sum_{n>=1} A168595(n)*x^n/n ), where A168595(n) = Sum_{k=0..2*n} binomial(n,k)*trinomial(n,k).

%F (2) A(x) = (1/x)*Series_Reversion( x*(1-x)^4/(1-x^3)^2 ).

%e G.f.: A(x) = 1 + 4*x + 26*x^2 + 202*x^3 + 1731*x^4 + 15780*x^5 +...

%e where A(x) = (1 - x^3*A(x)^3)^2 / (1 - x*A(x))^4.

%e The logarithm begins:

%e log(A(x)) = 4*x + 36*x^2/2 + 358*x^3/3 + 3748*x^4/4 + 40404*x^5/5 + 443886*x^6/6 + 4941654*x^7/7 +...+ A168595(n)*x^n/n +...

%o (PARI) {a(n) = local(A=1); A = (1/x)*serreverse( x*(1-x)^4/(1-x^3)^2 +x^2*O(x^n)); polcoeff(A,n)}

%o for(n=0,30,print1(a(n),", "))

%o (PARI) {A168595(n) = sum(k=0, 2*n, binomial(2*n, k) * polcoeff((1+x+x^2)^n, k) )}

%o {a(n) = local(A=1); A = exp( sum(k=1,n+1, A168595(k)*x^k/k) +x*O(x^n)); polcoeff(A,n)}

%o for(n=0,30,print1(a(n),", "))

%Y Cf. A168595, A106228, A064641, A253256.

%K nonn

%O 0,2

%A _Paul D. Hanna_, May 31 2015