A132986 Triangle, read by rows, where row n of T = row n-1 of T^n (shift right 1 column) with T(n,0)=T(n,1) for n>0.

1, 1, 1, 2, 2, 1, 12, 12, 6, 1, 240, 240, 120, 24, 1, 18480, 18480, 9360, 2040, 120, 1, 6708240, 6708240, 3466080, 801360, 55440, 720, 1, 14088352320, 14088352320, 7423763760, 1792667520, 136972080, 2202480, 5040, 1, 203200845886080

Offset

0,4

Links

Table of n, a(n) for n=0..36.

Example

Triangle begins:
1;
1, 1;
2, 2, 1;
12, 12, 6, 1;
240, 240, 120, 24, 1;
18480, 18480, 9360, 2040, 120, 1;
6708240, 6708240, 3466080, 801360, 55440, 720, 1;
14088352320, 14088352320, 7423763760, 1792667520, 136972080, 2202480, 5040, 1;
Matrix square T^2 begins:
1;
2, 1; <-- row 2 of T
6, 4, 1;
48, 36, 12, 1;
1248, 1008, 384, 48, 1;
127440, 108960, 45360, 6960, 240, 1; ...
Matrix cube T^3 begins:
1;
3, 1;
12, 6, 1; <-- row 3 of T
120, 72, 18, 1;
3840, 2592, 792, 72, 1;
486720, 359280, 125280, 14760, 360, 1; ...
Matrix fourth-power T^4 begins:
1;
4, 1;
20, 8, 1;
240, 120, 24, 1; <-- row 4 of T
9120, 5280, 1344, 96, 1;
1378560, 891840, 266400, 25440, 480, 1; ...

Prog

(PARI) {T(n, k)=local(M=if(n==0, [1], matrix(n+1, n+1, r, c, if(r>=c&r<=n, T(r-1, c-1))))); if(n==0, 1, if(k==0, T(n, 1), (M^n)[n, k]))}

Crossrefs

Cf. A132987 (column 0).

Sequence in context: A100942 A132471 A130528 * A019112 A048660 A019227

Adjacent sequences: A132983 A132984 A132985 * A132987 A132988 A132989

Keyword

nonn,tabl

Author

Paul D. Hanna, Sep 07 2007

Status

approved