0,7

T(n, n)= 1; T(n+1, n)= n; T(n+2, n)= A002061(n+1)= n^2 + n + 1; T(n+3, n)= n^3 + 3*n^2 + 5*n + 2.

T(n, k) = (k + 1)*T(n, k + 1)-T(n-1, k); T(n, n)= 1; T(n, k)= 0, if k>n. T(n, k) = (n-1)*T(n-1, k) + (n-k-1)*T(n-2, k). k!*T(n, k) = A068106(n+1, k+1). Sum(k>=0; T(n, k) = A003470(n+1).

T(n, k) = 1/k! * Sum_{j>=0} (-1)^j*binomial(n-k, j)*(n-j)!. - Philippe DELEHAM, Jun 13 2005

1; 0, 1; 1, 1, 1; 2, 3, 2, 1; 9, 11, 7, 3, 1; 44, 53, 32, 13, 4, 1; ...

Formatted as a square array:

1 3 7 13 21 31 43 57 which equals A002061

2 11 32 71 134 227 356 which equals A094792

9 53 181 465 1001 1909 which equals A094793

44 309 1214 3539 8544 which equals A094794

265 2119 9403 30637 which equals A023043

1854 16687 82508 which equals A023044

14833 148329 which equals A023045

Formatted as a triangular array (mirror of A076731):

1

0 1

1 1 1

2 3 2 1

9 11 7 3 1

44 53 32 13 4 1

265 309 181 71 21 5 1

1854 2119 1214 465 134 31 6 1

14833 16687 9403 3539 1001 227 43 7 1

133496 148329 82508 30637 8544 1909 356 57 8 1

Columns: A000166, A000155, AOOO153, A000261, A001909, A001910.

Cf. A068106 A003470 AOO2061. Mirror image of A076731.

Sequence in context: A062323 A020858 A090664 this_sequence A076224 A114729 A049342

Adjacent sequences: A086761 A086762 A086763 this_sequence A086765 A086766 A086767

easy,nonn,tabl

DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Aug 02 2003

More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Mar 28 2005

Additional comments from Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 30 2006