|
|
A155858
|
|
Diagonal sums of triangle A155856.
|
|
2
|
|
|
1, 1, 3, 9, 35, 168, 967, 6538, 50831, 446919, 4383861, 47451921, 561715093, 7217604520, 100031995789, 1487319385140, 23613262336093, 398673670050021, 7132188802005991, 134766129577134553, 2681929390235577831
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
FORMULA
|
G.f.: 1/(1 -x^2 -x/(1 -x^2 -x/(1 -x^2 -2*x/(1 -x^2 -2*x/(1 -x^2 -3*x/(1 -x^2 -3*x/(1 - ... (continued fraction);
a(n) = Sum_{k=0..floor(n/2)} binomial(2*n-3*k, k)*(n-2*k)!.
Conjecture: a(n) -(n-1)*a(n-1) -(n-2)*a(n-2) +(n-3)*a(n-3) +(n-10)*a(n-4) -5*a(n-5) +3*a(n-6) +3*a(n-7) = 0. - R. J. Mathar, Feb 05 2015
a(n) ~ n! * (1 + 2/n + 1/n^2 - 2/(3*n^3) - 22/(3*n^4) - 491/(15*n^5) - 11467/(90*n^6) - ...). - Vaclav Kotesovec, Jun 05 2021
|
|
MATHEMATICA
|
Table[Sum[Binomial[2*n-3*k, k]*(n-2*k)!, {k, 0, Floor[n/2]}], {n, 0, 30}] (* G. C. Greubel, Jun 05 2021 *)
|
|
PROG
|
(Sage) [sum( binomial(2*n-3*k, k)*factorial(n-2*k) for k in (0..n//2) ) for n in (0..30)] # G. C. Greubel, Jun 05 2021
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|