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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A000658 Strehl's sequence "C_n^(3)". 3
1, 4, 68, 1732, 51076, 1657904, 57793316, 2117525792, 80483121028, 3147565679824, 125937573689968, 5133632426499152, 212530848994367524, 8914634034287235856, 378138515326996979168, 16196097181014298854032 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

Volker Strehl, Binomial identities - combinatorial and algorithmic aspects. Trends in discrete mathematics. Discrete Math. 136 (1994), no. 1-3, 309-346.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..100

Vaclav Kotesovec, Recurrence (of order 6)

FORMULA

Sum binomial(n, k)^2 * binomial(2k, k)^2 * binomial(2k, n-k); k=0..n.

a(n) ~ 7^(2*n+5/2) / (20 * sqrt(15) * Pi^2 * n^2). - Vaclav Kotesovec, Mar 09 2014

MAPLE

A000658:=n->add(binomial(n, k)^2*binomial(2*k, k)^2*binomial(2*k, n-k), k=0..n): seq(A000658(n), n=0..15); # Wesley Ivan Hurt, Sep 19 2014

MATHEMATICA

Table[Sum[Binomial[n, k]^2 Binomial[2k, k]^2 Binomial[2k, n-k], {k, 0, n}], {n, 0, 25}] (* Harvey P. Dale, Oct 19 2011 *)

PROG

(PARI) a(n)=sum(k=1, n, binomial(n, k)^2 * binomial(2k, k)^2 * binomial(2k, n-k)) \\ Charles R Greathouse IV, Sep 19 2014

(Haskell)

a000658 n = sum $ map c3 [0..n] where

   c3 k = (a007318' n k)^2 * (a007318' (2*k) k)^2 * a007318' (2*k) (n-k)

-- Reinhard Zumkeller, May 20 2015

CROSSREFS

Third row of array A094424.

Cf. A007318.

Sequence in context: A323276 A141032 A156084 * A156470 A326288 A302115

Adjacent sequences:  A000655 A000656 A000657 * A000659 A000660 A000661

KEYWORD

nonn,easy,nice

AUTHOR

Don Knuth

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 October 15 15:14 EDT 2019. Contains 328030 sequences. (Running on oeis4.)