login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A217280 a(n) = Sum_{k=0..n} binomial(n,k)^3 * 2^k * 3^(n-k). 1
1, 5, 61, 845, 12865, 206525, 3434005, 58542125, 1016757025, 17915319125, 319316172781, 5744962350605, 104168557434241, 1901265562745645, 34897397882019685, 643662507367299725, 11922610595971162945, 221673143774064873125, 4135241181985049252125 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

5 divides a(n) except when a(n) == 1 (mod 5), which occurs only when the base 5 representation of n consists solely of digits '0' and '2' (conjecture). Positions n at which a(n) == 1 (mod 5) begin: [0, 2, 10,12, 50,52,60,62, 250,252,260,262,300,302,310,312, 1250,1252,1260,1262,1300,1302,1310,1312,1500,1502,1510,1512, 1550,1552,1560,1562, ...].

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

V. Kotesovec, Asymptotic of a sums of powers of binomial coefficients * x^k, Sep 20 2012

FORMULA

a(n) ~ 3^n*(1+(2/3)^(1/3))^(3*n+2)/(2^(4/3)*3^(1/6)*Pi*n)*(1+((2/3)^(1/3)+(3/2)^(1/3)-5)/(9*n)). - Vaclav Kotesovec, Sep 30 2012

G.f.: hypergeom([1/3, 2/3],[1],162*x^2/(1-5*x)^3)/(1-5*x). - Mark van Hoeij, Apr 11 2014

MATHEMATICA

Table[Sum[Binomial[n, k]^3*2^k*3^(n-k), {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Sep 30 2012 *)

PROG

(PARI) {a(n)=sum(k=0, n, binomial(n, k)^3*2^k*3^(n-k))}

for(n=0, 21, print1(a(n), ", "))

CROSSREFS

Sequence in context: A099666 A189444 A217811 * A236955 A064328 A012060

Adjacent sequences:  A217277 A217278 A217279 * A217281 A217282 A217283

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Sep 29 2012

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 February 25 08:33 EST 2021. Contains 341606 sequences. (Running on oeis4.)