A187044 -id:A187044 - cp's OEIS frontend

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

Vincenzo Librandi, Dec 25 2012

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

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

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

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

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

A070895 Triangle read by rows where T(n+1,k)=T(n,k)+n*T(n-1,k) starting with T(n,n)=1 and T(n,k)=0 if n

Original entry on oeis.org

1, 1, 1, 2, 1, 1, 4, 3, 1, 1, 10, 6, 4, 1, 1, 26, 18, 8, 5, 1, 1, 76, 48, 28, 10, 6, 1, 1, 232, 156, 76, 40, 12, 7, 1, 1, 764, 492, 272, 110, 54, 14, 8, 1, 1, 2620, 1740, 880, 430, 150, 70, 16, 9, 1, 1, 9496, 6168, 3328, 1420, 636, 196, 88, 18, 10, 1, 1, 35696, 23568

Offset: 0

Henry Bottomley, May 23 2002

For n>k+1, T(n,k) is a multiple of k+2.

Eigentriangle of inverse of (-1)^(n-k)*A094587. Row sums are A187044. - Paul Barry, Mar 02 2011

			Rows start: 1; 1,1; 2,1,1; 4,3,1,1; 10,6,4,1,1; etc.
Triangle begins
1,
1, 1,
2, 1, 1,
4, 3, 1, 1,
10, 6, 4, 1, 1,
26, 18, 8, 5, 1, 1,
76, 48, 28, 10, 6, 1, 1,
232, 156, 76, 40, 12, 7, 1, 1
Production matrix begins
1, 1,
1, 0, 1,
1, 1, 0, 1,
2, 1, 1, 0, 1,
4, 3, 1, 1, 0, 1,
10, 6, 4, 1, 1, 0, 1,
26, 18, 8, 5, 1, 1, 0, 1,
76, 48, 28, 10, 6, 1, 1, 0, 1,
232, 156, 76, 40, 12, 7, 1, 1, 0, 1
Inverse begins
1,
-1, 1,
-1, -1, 1,
0, -2, -1, 1,
0, 0, -3, -1, 1,
0, 0, 0, -4, -1, 1,
0, 0, 0, 0, -5, -1, 1,
0, 0, 0, 0, 0, -6, -1, 1
- _Paul Barry_, Mar 02 2011

Columns include A000085, A000932, A059480. Right hand columns effectively include A000012 (twice), A000027, A005843, A028552. Cf. A062323 for a triangle with similar formulas.

T(n, k+1)=(T(n, k-1)-T(n-1, k))/k for 0

Showing 1-2 of 2 results.

cp's OEIS Frontend

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

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