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

0,3

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, n-k))^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