

A225328


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


2



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

0,3


COMMENTS

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


LINKS

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


FORMULA

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


EXAMPLE

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 + ...


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 *)


PROG

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


CROSSREFS

Cf. A168599, A002426.
Sequence in context: A110695 A157589 A055601 * A203745 A012812 A266881
Adjacent sequences: A225325 A225326 A225327 * A225329 A225330 A225331


KEYWORD

nonn


AUTHOR

Paul D. Hanna, Aug 03 2013


STATUS

approved



