A155858 Diagonal sums of triangle A155856.

1, 1, 3, 9, 35, 168, 967, 6538, 50831, 446919, 4383861, 47451921, 561715093, 7217604520, 100031995789, 1487319385140, 23613262336093, 398673670050021, 7132188802005991, 134766129577134553, 2681929390235577831

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..440

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

Cf. A155856.

Sequence in context: A101880 A222398 A107894 * A000834 A005346 A129094

Adjacent sequences: A155855 A155856 A155857 * A155859 A155860 A155861

Keyword

easy,nonn

Author

Paul Barry, Jan 29 2009

Status

approved