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 A052553 Square array of binomial coefficients T(n,k) = binomial(n,k), n >= 0, k >= 0, read by antidiagonals. 12
 1, 1, 0, 1, 1, 0, 1, 2, 0, 0, 1, 3, 1, 0, 0, 1, 4, 3, 0, 0, 0, 1, 5, 6, 1, 0, 0, 0, 1, 6, 10, 4, 0, 0, 0, 0, 1, 7, 15, 10, 1, 0, 0, 0, 0, 1, 8, 21, 20, 5, 0, 0, 0, 0, 0, 1, 9, 28, 35, 15, 1, 0, 0, 0, 0, 0, 1, 10, 36, 56, 35, 6, 0, 0, 0, 0, 0, 0, 1, 11, 45, 84, 70, 21, 1, 0, 0, 0, 0, 0, 0, 1, 12, 55 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS Another version of Pascal's triangle A007318. As a triangle read by rows, it is (1,0,0,0,0,0,0,0,0,...) DELTA (0,1,-1,0,0,0,0,0,0,0,0,...) where DELTA is the operator defined in A084938 and it is the Riordan array (1/(1-x), x^2/(1-x)). The row sums of this triangle are F(n+1) = A000045(n+1). - Philippe Deléham, Dec 11 2011 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..5459 FORMULA As a triangle: T(n,k) = A026729(n,n-k). G.f. of the triangular version: 1/(1-x-x^2*y). - R. J. Mathar, Aug 11 2015 EXAMPLE Array begins: 1 0  0  0 0 0 ... 1 1  0  0 0 0 ... 1 2  1  0 0 0 ... 1 3  3  1 0 0 ... 1 4  6  4 1 0 ... 1 5 10 10 5 1 ... As a triangle, this begins: 1 1, 0 1, 1,  0 1, 2,  0, 0 1, 3,  1, 0, 0 1, 4,  3, 0, 0, 0 1, 5,  6, 1, 0, 0, 0 1, 6, 10, 4, 0, 0, 0, 0 MAPLE with(combinat): for s from 0 to 20 do for n from s to 0 by -1 do printf(`%d, `, binomial(n, s-n)) od:od: # James A. Sellers, Mar 17 2000 MATHEMATICA Flatten[ Table[ Binomial[n-k , k], {n, 0, 13}, {k, 0, n}]]  (* Jean-François Alcover, Dec 05 2012 *) PROG (PARI) T(n, k) = binomial(n, k) \\ Charles R Greathouse IV, Feb 07 2017 (MAGMA) /* As triangle */ [[Binomial(n-k, k): k in [0..n]]: n in [0.. 15]]; // Vincenzo Librandi, Feb 08 2017 CROSSREFS The official entry for Pascal's triangle is A007318. See also A026729. Cf. A052509, A054123, A054124, A008949. Sequence in context: A216599 A114510 A077029 * A290054 A290430 A290429 Adjacent sequences:  A052550 A052551 A052552 * A052554 A052555 A052556 KEYWORD nonn,tabl,easy,nice AUTHOR N. J. A. Sloane, Mar 17 2000 STATUS approved

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Last modified October 22 18:38 EDT 2018. Contains 316500 sequences. (Running on oeis4.)