login
A157113
Triangle, read by rows, T(n,k) = binomial(n*(n-k)*k, k) + binomial(n*(n-k)*k, n -k).
1
2, 1, 1, 1, 4, 1, 1, 21, 21, 1, 1, 232, 240, 232, 1, 1, 4865, 4495, 4495, 4865, 1, 1, 142536, 195708, 49608, 195708, 142536, 1, 1, 5245828, 12105429, 2024785, 2024785, 12105429, 5245828, 1, 1, 231917456, 927052864, 190858864, 21336000, 190858864, 927052864, 231917456, 1
OFFSET
0,1
COMMENTS
Row sums are: {2, 2, 6, 44, 706, 18722, 726098, 38752086, 2720994370, 241584879476, 26221233537242, ...}.
FORMULA
T(n,k) = binomial(n*(n-k)*k, k) + binomial(n*(n-k)*k, n-k).
EXAMPLE
Triangle begins as:
2;
1, 1;
1, 4, 1;
1, 21, 21, 1;
1, 232, 240, 232, 1;
1, 4865, 4495, 4495, 4865, 1;
1, 142536, 195708, 49608, 195708, 142536, 1;
1, 5245828, 12105429, 2024785, 2024785, 12105429, 5245828, 1;
MAPLE
b:=binomial; seq(seq( b(n*(n-k)*k, k) + b(n*(n-k)*k, n-k), k=0..n), n=0..10); # G. C. Greubel, Nov 29 2019
MATHEMATICA
Table[Binomial[n*(n-k)*k, k] + Binomial[n*(n-k)*k, n-k], {n, 0, 10}, {k, 0, n}]//Flatten
PROG
(PARI) my(b=binomial); T(n, k) = b(n*(n-k)*k, k) + b(n*(n-k)*k, n-k); \\ G. C. Greubel, Nov 29 2019
(Magma) B:=Binomial; [B(n*(n-k)*k, k) + B(n*(n-k)*k, n-k): k in [0..n], n in [0..10]]; // G. C. Greubel, Nov 29 2019
(Sage) b=binomial; [[b(n*(n-k)*k, k) + b(n*(n-k)*k, n-k) for k in (0..n)] for n in (0..10)] # G. C. Greubel, Nov 29 2019
(GAP) B:=Binomial;; Flat(List([0..10], n-> List([0..n], k-> B(n*(n-k)*k, k) + B(n*(n-k)*k, n-k) ))); # G. C. Greubel, Nov 29 2019
CROSSREFS
Sequence in context: A156786 A156141 A174555 * A214712 A213330 A139320
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula, Feb 23 2009
STATUS
approved