|
%I #14 Feb 28 2017 22:35:45
%S 1,1,9,343,130321,345025251,7858047974841,1447930954097073657,
%T 2255178731296086753063201,29588424532574699588724679418659,
%U 3308916781795356089160906125431831800049,3166064605712293355286523525163381509588445189997
%N a(n) = A002426(n)^n, where A002426 is the central trinomial coefficients.
%C Logarithmic derivative of A168599 (upon ignoring the initial term, a(0), of this sequence).
%H G. C. Greubel, <a href="/A225328/b225328.txt">Table of n, a(n) for n = 0..46</a>
%F L.g.f.: Sum_{n>=1} a(n)*x^n/n = log( Sum_{n>=0} A168599(n)*x^n ).
%e L.g.f.: L(x) = x + 9*x^2/2 + 343*x^3/3 + 130321*x^4/4 + 345025251*x^5/5 + ...
%e where exponentiation is an integer series:
%e exp(L(x)) = 1 + x + 5*x^2 + 119*x^3 + 32707*x^4 + 69038213*x^5 + 1309743837515*x^6 + ... + A168599(n)*x^n + ...
%t a[n_] := If[n < 0, 0, 3^n Hypergeometric2F1[1/2, -n, 1, 4/3]]; Table[a[n]^n, {n, 0, 50}] (* _G. C. Greubel_, Feb 27 2017 *)
%o (PARI) {a(n)=sum(k=0,n, binomial(n, k)*binomial(k, n-k))^n}
%o for(n=0,20,print1(a(n),", "))
%Y Cf. A168599, A002426.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Aug 03 2013
|
