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 A126450 Triangle, read by rows, where T(n,k) = C( C(n+2,3) - C(k+2,3) + 1, n-k) for n>=k>=0. 9
 1, 2, 1, 10, 4, 1, 165, 45, 7, 1, 5985, 1140, 136, 11, 1, 376992, 52360, 4960, 325, 16, 1, 36288252, 3819816, 292825, 16215, 666, 22, 1, 4935847320, 406481544, 25621596, 1215450, 43680, 1225, 29, 1, 899749479915, 59487568920, 3127595016, 128164707 (list; table; graph; refs; listen; history; text; internal format)
 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 FORMULA T(n,k) = C( n*(n+1)*(n+2)/3! - k*(k+1)*(k+2)/3! + 1, n-k) for n>=k>=0. EXAMPLE Formula: T(n,k) = C( C(n+2,3) - C(k+2,3) + 1, n-k) is illustrated by: T(n=4,k=1) = C( C(6,3) - C(3,3) + 1, n-k) = C(20,3) = 1140; T(n=4,k=2) = C( C(6,3) - C(4,3) + 1, n-k) = C(17,2) = 136; T(n=5,k=2) = C( C(7,3) - C(4,3) + 1, n-k) = C(32,3) = 4960. Triangle begins: 1; 2, 1; 10, 4, 1; 165, 45, 7, 1; 5985, 1140, 136, 11, 1; 376992, 52360, 4960, 325, 16, 1; 36288252, 3819816, 292825, 16215, 666, 22, 1; 4935847320, 406481544, 25621596, 1215450, 43680, 1225, 29, 1; ... PROG (PARI) T(n, k)=binomial(n*(n+1)*(n+2)/3!-k*(k+1)*(k+2)/3!+1, n-k) CROSSREFS Columns: A126451, A126452; A126453 (row sums); variants: A126445, A126454, A126457, A107867. Sequence in context: A105615 A136216 A121334 * A235608 A112333 A066868 Adjacent sequences:  A126447 A126448 A126449 * A126451 A126452 A126453 KEYWORD nonn,tabl AUTHOR Paul D. Hanna, Dec 27 2006 STATUS approved

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Last modified July 2 17:09 EDT 2022. Contains 355029 sequences. (Running on oeis4.)