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A126445 Triangle, read by rows, where T(n,k) = C( C(n+2,3) - C(k+2,3), n-k) for n>=k>=0. 10
1, 1, 1, 6, 3, 1, 120, 36, 6, 1, 4845, 969, 120, 10, 1, 324632, 46376, 4495, 300, 15, 1, 32468436, 3478761, 270725, 15180, 630, 21, 1, 4529365776, 377447148, 24040016, 1150626, 41664, 1176, 28, 1, 840261910995, 56017460733, 2967205528, 122391522 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

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!, n-k) for n>=k>=0.

EXAMPLE

Formula: T(n,k) = C( C(n+2,3) - C(k+2,3), n-k) is illustrated by:

T(n=4,k=1) = C( C(6,3) - C(3,3), n-k) = C(19,3) = 969;

T(n=4,k=2) = C( C(6,3) - C(4,3), n-k) = C(16,2) = 120;

T(n=5,k=2) = C( C(7,3) - C(4,3), n-k) = C(31,3) = 4495.

Triangle begins:

1;

1, 1;

6, 3, 1;

120, 36, 6, 1;

4845, 969, 120, 10, 1;

324632, 46376, 4495, 300, 15, 1;

32468436, 3478761, 270725, 15180, 630, 21, 1;

4529365776, 377447148, 24040016, 1150626, 41664, 1176, 28, 1; ...

PROG

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

CROSSREFS

Columns: A126446, A126447, A126448; A126449 (row sums); variants: A126450, A126454, A126457, A107862.

Sequence in context: A182227 A108451 A122178 * A277435 A033326 A068996

Adjacent sequences:  A126442 A126443 A126444 * A126446 A126447 A126448

KEYWORD

nonn,tabl

AUTHOR

Paul D. Hanna, Dec 27 2006

STATUS

approved

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Last modified November 22 00:32 EST 2019. Contains 329383 sequences. (Running on oeis4.)