OFFSET
0,2
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
G. Kreweras, Sur les hiérarchies de segments, Cahiers du Bureau Universitaire de Recherche Opérationnelle, Institut de Statistique, Université de Paris, #20 (1973).
G. Kreweras, Sur les hiérarchies de segments, Cahiers du Bureau Universitaire de Recherche Opérationnelle, Institut de Statistique, Université de Paris, #20 (1973). (Annotated scanned copy)
FORMULA
a(n) = (4/n)*sum(binomial(n, j)*binomial(n+3+j, n-1), j=0..n) (n>0). - Emeric Deutsch, Aug 19 2004
Recurrence: n*(n+4)*a(n) = (5*n^2+14*n+21)*a(n-1) + (5*n^2-4*n+12)*a(n-2) - (n-3)*(n+1)*a(n-3). - Vaclav Kotesovec, Oct 05 2012
a(n) ~ 2*sqrt(816+577*sqrt(2))*(3+2*sqrt(2))^n/(sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 05 2012
G.f.: (x^4-8*x^3+16*x^2-8*x+1+sqrt(x^2-6*x+1)*(x-1)*(x^2-4*x+1))/(2*x^4). - Mark van Hoeij, Apr 16 2013
MAPLE
1, seq(4*sum(binomial(n, j)*binomial(n+3+j, n-1), j=0..n)/n, n=1..17);
MATHEMATICA
Flatten[{1, RecurrenceTable[{n*(n+4)*a[n] == (5*n^2+14*n+21)*a[n-1] + (5*n^2-4*n+12)*a[n-2] - (n-3)*(n+1)*a[n-3], a[1] == 8, a[2] == 48, a[3] == 264}, a, {n, 25}]}] (* Vaclav Kotesovec, Oct 05 2012 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Vincenzo Librandi, May 03 2013
STATUS
approved