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

0,3

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

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

Prog

(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)!))))

Crossrefs

Cf. A007583, A092469.

Sequence in context: A152751 A369953 A162654 * A347108 A027158 A251781

Adjacent sequences: A092465 A092466 A092467 * A092469 A092470 A092471

Keyword

nonn

Author

Benoit Cloitre, Mar 25 2004

Status

approved