A193361 a(0)=0, a(1)=0; for n>1, a(n) = a(n-1) + (n-3)*a(n-2) + 1.

0, 0, 1, 2, 4, 9, 22, 59, 170, 525, 1716, 5917, 21362, 80533, 315516, 1281913, 5383622, 23330405, 104084736, 477371217, 2246811730, 10839493637, 53528916508, 270318789249, 1394426035918, 7341439399397, 39413238225512, 215607783811041, 1200938739448842

Offset: 0

Author

Vincenzo Librandi, Dec 25 2012

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..800

Crossrefs

Cf. A185108, A185109, A185308, A185309, A186738, A186739, A213720.

Programs

Magma

[n le 2 select 0 else Self(n-1)+(n-4)*Self(n-2) + 1: n in [1..30]];

Mathematica

RecurrenceTable[{a[1]==0,a[2]==0,a[n]==a[n-1]+(n-4) a[n-2]+1},a,{n,30}]

Formula

a(0)=a(1)=0, a(2)=1, a(n) = 2*a(n-1)+(n-4)*a(n-2)-(n-4)*a(n-3).

a(n) ~ (sqrt(Pi)+sqrt(2))/2 * n^(n/2-1)*exp(sqrt(n)-n/2-1/4) * (1-17/(24*sqrt(n))). - Vaclav Kotesovec, Dec 27 2012

a(n) = A187044(n-2). - Vaclav Kotesovec, Feb 14 2014