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!)
A014316 Convolution of Catalan numbers and squares. 1
0, 1, 5, 15, 38, 93, 236, 641, 1869, 5779, 18663, 62179, 211909, 734651, 2581317, 9169247, 32867726, 118729269, 431756336, 1579232417, 5806059402, 21443620901, 79522304354, 295990940421, 1105391706392, 4140688363241, 15553731459744, 58573820469505 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

FORMULA

a(n) ~ 5 * 2^(2*n+2) / (27 * sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Mar 08 2018

G.f.: (1 + x)*(1 - sqrt(1 - 4*x))/(2*(1 - x)^3). - Ilya Gutkovskiy, Mar 21 2018

MAPLE

a:= proc(n) option remember; `if`(n<3, n*(3*n-1)/2,

      ((60*n^3-232*n^2+264*n-90) *a(n-1)

      -(90*n^3-308*n^2+257*n-24) *a(n-2)

      +2*(2*n-3)*(10*n^2-12*n+1) *a(n-3))/ (n*(10*n^2-32*n+23)))

    end:

seq(a(n), n=0..30);  # Alois P. Heinz, Nov 10 2013

MATHEMATICA

a[n_] := Sum[CatalanNumber[k]*(k-n)^2, {k, 0, n}]; Table[a[n], {n, 0, 30}] (* Jean-Fran├žois Alcover, Mar 16 2017 *)

PROG

(PARI) a(n) = sum(i=0, n, i^2*(2*(n-i))!/((n-i)!*(n-i+1)!)); \\ Michel Marcus, Nov 10 2013

CROSSREFS

Cf. A000108, A000290.

Sequence in context: A050488 A142964 A188282 * A075717 A062487 A084447

Adjacent sequences:  A014313 A014314 A014315 * A014317 A014318 A014319

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

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 April 3 17:03 EDT 2020. Contains 333197 sequences. (Running on oeis4.)