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A118968 a(4n+k)=(k+1)*binomial(5n+k,n)/(4n+k+1), k=0,..3. 5

%I

%S 1,1,1,1,1,2,3,4,5,11,18,26,35,80,136,204,285,665,1155,1771,2530,5980,

%T 10530,16380,23751,56637,100688,158224,231880,556512,996336,1577532,

%U 2330445,5620485,10116873,16112057,23950355,57985070,104819165

%N a(4n+k)=(k+1)*binomial(5n+k,n)/(4n+k+1), k=0,..3.

%C Row sums of Riordan array (1,x(1-x^4))^(-1). a(4n)=A002294(n),a(4n+1)=A118969(n),a(4n+2)=A118970(n),a(4n+3)=A118971(n).

%F G.f. satisfies: A(x) = 1 + x*A(x)^2*A(-x)*A(I*x)*A(-I*x). - _Paul D. Hanna_, Jun 04 2012

%F G.f. satisfies: A(x) = 1 + x*A(x)*G(x^4) where G(x) = 1 + x*G(x)^5 is the g.f. of A002294. - _Paul D. Hanna_, Jun 04 2012

%o (PARI) {a(n)=local(A=1+x+x*O(x^n));for(i=1,n,A=1+x*A^2*subst(A,x,-x)*subst(A,x,I*x)*subst(A,x,-I*x));polcoeff(A,n)} \\ _Paul D. Hanna_, Jun 04 2012

%o (PARI) {a(n)=local(A=1+x);for(i=1,n,A=1+x*A*exp(sum(m=1,n\4,4*polcoeff(log(A+x*O(x^n)),4*m)*x^(4*m))+x*O(x^n)));polcoeff(A,n)} \\ _Paul D. Hanna_, Jun 04 2012

%Y Cf. A124753, A002294.

%K easy,nonn

%O 0,6

%A _Paul Barry_, May 07 2006

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Last modified September 26 13:34 EDT 2021. Contains 347668 sequences. (Running on oeis4.)