cp's OEIS Frontend

A216586 G.f.: exp( Sum_{n>=1} A002426(n)/2 * A002426(n) * x^n/n ), where A002426 is the central binomial coefficients and A002426 is the central trinomial coefficients.

%I A216586 #8 Nov 21 2024 14:54:24
%S A216586 1,1,5,28,202,1579,13375,118858,1098458,10453452,101872926,1012109860,
%T A216586 10218226307,104570617520,1082633236498,11321654913838,
%U A216586 119438468577559,1269787015989428,13592294300856138,146390465351654178,1585337895099162317,17253991887494062080
%N A216586 G.f.: exp( Sum_{n>=1} A002426(n)/2 * A002426(n) * x^n/n ), where A002426 is the central binomial coefficients and A002426 is the central trinomial coefficients.
%F A216586 Self-convolution yields A216585.
%e A216586 G.f.: A(x) = 1 + x + 5*x^2 + 28*x^3 + 202*x^4 + 1579*x^5 + 13375*x^6 +...
%e A216586 such that
%e A216586 log(A(x)) = 1*1*x + 3*3*x^2/2 + 10*7*x^3/3 + 35*19*x^4/4 + 126*51*x^5/5 + 462*141*x^6/6 +...+ A001700(n)*A002426(n)*x^n/n +...
%o A216586 (PARI) {a(n)=polcoeff(exp(sum(m=1,n+1,binomial(2*m,m)/2*polcoeff((1+x+x^2)^m,m)*x^m/m+x*O(x^n))),n)}
%o A216586 for(n=0,30,print1(a(n),", "))
%Y A216586 Cf. A216585, A002426, A001700, A000984.
%K A216586 nonn
%O A216586 0,3
%A A216586 _Paul D. Hanna_, Sep 09 2012