A092468 a(n) = Sum_{i+j+k=n, 0<=i<=j<=k<=n} (n+2k)!/(i! * j! * (3*k)!).

1, 1, 3, 24, 71, 366, 2142, 8128, 40063, 223182, 919600, 4477496, 24423998, 104469379, 508145588, 2726623094, 11936904927, 58101760966, 307770506832, 1369729219470, 6671075408724, 34985537652681, 157621462924548

Offset: 0

Author

Benoit Cloitre, Mar 25 2004

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..1000 (terms 0..200 from Seiichi Manyama)
• Vaclav Kotesovec, Plot a(n+1)/a(n) for n = 1..999

Crossrefs

Cf. A007583, A092469.

Programs

PARI

a(n)=sum(i=0,n,sum(j=0,i,sum(k=0,j,if(i+j+k-n,0,(n+2*k)!/i!/j!/(3*k)!))))

Formula

Conjecture: a(n+1)/a(n) tends to (73 + 6*sqrt(87))^(1/3)/3 + 13/(3*(73 + 6*sqrt(87))^(1/3)) + 7/3 = 4.875129794... - Vaclav Kotesovec, Oct 31 2021