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!)
A025758 5th-order Vatalan numbers (generalization of Catalan numbers). 2
1, 1, 11, 171, 3056, 58916, 1191376, 24896436, 532911346, 11617952106, 256966100966, 5750337968926, 129926216608236, 2959472057112396, 67877180959091156, 1566072624078270516, 36319953436423545851 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.

FORMULA

G.f.: 5 / (4+(1-25*x)^(1/5)).

a(n) = sum(m=1..n-1, 5^(n-m)*m/n * sum(k=1..n-m, binomial(n+k-1,n-1) * sum(i=0..k, binomial(k,i) * 2^(k-i) * sum(j=0..i, binomial(j,-3*i+n-m-k+2*j) * (-1)^(j-i)*5^(j-i)*(-2)^(3*i-n+m+k-j) * binomial(i,j)))))+1. - Vladimir Kruchinin, Feb 09 2011

Conjecture: 41*n*(n-1)*(n-2)*(n-3)*a(n) -3*(1367*n-4100)*(n-1)*(n-2)*(n-3)*a(n-1) +50*(n-2)*(n-3)*(3077*n^2-21533*n+38136)*a(n-2) -250*(n-3)*(10265*n^3-123135*n^2+494446*n-664572)*a(n-3) +1875*(8575*n^4-154250*n^3+1039765*n^2-3112730*n+3491808)*a(n-4) -625*(5*n-22)*(5*n-21)*(5*n-24)*(5*n-23)*a(n-5)=0. - R. J. Mathar, Jul 28 2014

MAPLE

# Based on Tani Akinari's formula.

h := (n, j) -> ((-1)^n/(-4)^j)*binomial(j/5, n+1)*hypergeom([1, n+1-j/5], [n+2], 1025): a := n -> 2^8*5^(2*n+1)*add(h(n, j), j=1..4):

seq(round(evalf(a(n), 64)), n=0..16); # Peter Luschny, Sep 21 2015

MATHEMATICA

Table[SeriesCoefficient[5/(4 + (1 - 25*x)^(1/5)), {x, 0, n}], {n, 0, 20}] (* Vincenzo Librandi, Dec 29 2012 *)

PROG

(Maxima) a(n):=(256/205)*41^(-n)*sum(sum((-4)^(-k)*(-1025)^m*binomial(k/5, m), k, 0, 4), m, 0, n);  /* Tani Akinari, Sep 16 2015  */

CROSSREFS

a(n), n >= 1, = row sums of triangle A049223.

Sequence in context: A205087 A064182 A139792 * A243677 A307168 A141955

Adjacent sequences:  A025755 A025756 A025757 * A025759 A025760 A025761

KEYWORD

nonn

AUTHOR

Olivier Gérard

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 27 11:07 EST 2021. Contains 341649 sequences. (Running on oeis4.)