A225328 a(n) = A002426(n)^n, where A002426 is the central trinomial coefficients.

1, 1, 9, 343, 130321, 345025251, 7858047974841, 1447930954097073657, 2255178731296086753063201, 29588424532574699588724679418659, 3308916781795356089160906125431831800049, 3166064605712293355286523525163381509588445189997

Offset: 0

Author

Paul D. Hanna, Aug 03 2013

Keywords

• nonn

Comments

Logarithmic derivative of A168599 (upon ignoring the initial term, a(0), of this sequence).

Examples

			L.g.f.: L(x) = x + 9*x^2/2 + 343*x^3/3 + 130321*x^4/4 + 345025251*x^5/5 + ...
where exponentiation is an integer series:
exp(L(x)) = 1 + x + 5*x^2 + 119*x^3 + 32707*x^4 + 69038213*x^5 + 1309743837515*x^6 + ... + A168599(n)*x^n + ...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..46

Crossrefs

Cf. A168599, A002426.

Programs

Mathematica

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 *)

PARI

{a(n)=sum(k=0,n, binomial(n, k)*binomial(k, n-k))^n}
for(n=0,20,print1(a(n),", "))

Formula

L.g.f.: Sum_{n>=1} a(n)*x^n/n = log( Sum_{n>=0} A168599(n)*x^n ).