A126457 Triangle, read by rows, where T(n,k) = C( C(n+2,3) - C(k+2,3) + 3, n-k) for n>=k>=0.

1, 4, 1, 21, 6, 1, 286, 66, 9, 1, 8855, 1540, 171, 13, 1, 501942, 66045, 5984, 378, 18, 1, 45057474, 4582116, 341055, 18424, 741, 24, 1, 5843355957, 470155077, 29034396, 1353275, 47905, 1326, 31, 1, 1029873432159, 66983637864, 3470108187, 140364532

Offset

0,2

Comments

Amazingly, A126460 = A126445^-1*A126450 = A126450^-1*A126454 = A126454^-1*A126457; and also A126465 = A126450*A126445^-1 = A126454*A126450^-1 = A126457*A126454^-1.

Links

Table of n, a(n) for n=0..39.

Formula

T(n,k) = C( n*(n+1)*(n+2)/3! - k*(k+1)*(k+2)/3! + 3, n-k) for n>=k>=0.

Example

Formula: T(n,k) = C( C(n+2,3) - C(k+2,3) + 3, n-k) is illustrated by:
T(n=4,k=1) = C( C(6,3) - C(3,3) + 3, n-k) = C(22,3) = 1540;
T(n=4,k=2) = C( C(6,3) - C(4,3) + 3, n-k) = C(19,2) = 171;
T(n=5,k=2) = C( C(7,3) - C(4,3) + 3, n-k) = C(34,3) = 5984.
Triangle begins:
1;
4, 1;
21, 6, 1;
286, 66, 9, 1;
8855, 1540, 171, 13, 1;
501942, 66045, 5984, 378, 18, 1;
45057474, 4582116, 341055, 18424, 741, 24, 1;
5843355957, 470155077, 29034396, 1353275, 47905, 1326, 31, 1; ...

Prog

(PARI) T(n, k)=binomial(n*(n+1)*(n+2)/3!-k*(k+1)*(k+2)/3!+3, n-k)

Crossrefs

Columns: A126458, A126459; variants: A126445, A126450, A126454, A107873.

Sequence in context: A182826 A144484 A121336 * A159841 A202550 A364760

Adjacent sequences: A126454 A126455 A126456 * A126458 A126459 A126460

Keyword

nonn,tabl

Author

Paul D. Hanna, Dec 27 2006

Status

approved