A092471 a(n) = Sum_{i+j+k=n, 0<=i<=n, 0<=j<=n, 0<=k<=n} (n+i+j)!/((i+j)! * j! * k!).

1, 5, 43, 495, 7281, 133173, 2945755, 76769759, 2306295265, 78492222693, 2985018589323, 125449316558415, 5773653823774929, 288808141870191765, 15601413322486382523, 905170780889312826303, 56136189828704013001665

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..200

Formula

From Vaclav Kotesovec, Oct 30 2021: (Start)

a(n) ~ 2^(2*n + 1/2) * n^n / exp(n - 3/2).

Recurrence: n*(2*n - 5)*a(n) = (2*n - 5)*(2*n - 1)*(2*n + 3)*a(n-1) - (2*n - 3)*(24*n^2 - 72*n + 29)*a(n-2) + (2*n - 9)*(2*n - 5)*(2*n - 1)*a(n-3) + (n-3)*(2*n - 1)*a(n-4). (End)

Prog

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

Crossrefs

Sequence in context: A301976 A083070 A191802 * A093620 A231277 A188365

Adjacent sequences: A092468 A092469 A092470 * A092472 A092473 A092474

Keyword

nonn

Author

Benoit Cloitre, Mar 25 2004

Status

approved