A102323 Triangle, read by rows, where T(n,k) = T(n,k-1) + (2*k+1)*T(n-1,k) for n>k>0, T(n,0)=1 and T(n,n) = T(n,n-1) for n>=0.

1, 1, 1, 1, 4, 4, 1, 13, 33, 33, 1, 40, 205, 436, 436, 1, 121, 1146, 4198, 8122, 8122, 1, 364, 6094, 35480, 108578, 197920, 197920, 1, 1093, 31563, 279923, 1257125, 3434245, 6007205, 6007205, 1, 3280, 161095, 2120556, 13434681, 51211376

Offset

0,5

Comments

Main diagonal is A102321, which is column 0 of triangle A102320.

Links

Table of n, a(n) for n=0..41.

Example

T(5,2) = 1146 = 1*1 + 3*40 + 5*205 = 1*T(4,0) + 3*T(4,1) + 5*T(4,2).
T(5,2) = 1146 = 121 + 5*205 = T(5,1) + (2*2+1)*T(4,2).
T(5,3) = 4198 = 1146 + 7*436 = T(5,2) + (2*3+1)*T(4,3).
Rows begin:
[1],
[1,1],
[1,4,4],
[1,13,33,33],
[1,40,205,436,436],
[1,121,1146,4198,8122,8122],
[1,364,6094,35480,108578,197920,197920],
[1,1093,31563,279923,1257125,3434245,6007205,6007205],...

Prog

(PARI) T(n, k)=if(n<k|k<0, 0, if(n==0|k==0, 1, T(n, k-1)+(2*k+1)*T(n-1, k)))

Crossrefs

Cf. A102316, A102321, A102320.

Sequence in context: A106026 A096078 A140313 * A145902 A124028 A123966

Adjacent sequences: A102320 A102321 A102322 * A102324 A102325 A102326

Keyword

nonn,tabl

Author

Paul D. Hanna, Jan 05 2005

Status

approved