login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 12 09:36 EST 2019. Contains 329953 sequences. (Running on oeis4.)