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 A060543 Triangle, read by antidiagonals, where T(n,k) = C(n+n*k+k, n*k+k). 11
 1, 1, 1, 1, 3, 1, 1, 10, 5, 1, 1, 35, 28, 7, 1, 1, 126, 165, 55, 9, 1, 1, 462, 1001, 455, 91, 11, 1, 1, 1716, 6188, 3876, 969, 136, 13, 1, 1, 6435, 38760, 33649, 10626, 1771, 190, 15, 1, 1, 24310, 245157, 296010, 118755, 23751, 2925, 253, 17, 1, 1, 92378, 1562275 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Main diagonal is A108288. Antidiagonal sums is A108289. Inverse binomial transforms of each row give triangle A108290. G.f. of row n multiplied by (1-x)^(n+1) equals g.f. of row n of triangle A108267 (rows sums of A108267 equal (n+1)^n). LINKS Harry J. Smith, Table of n, a(n) for n=0..252 FORMULA a(n) = A060539(n, k)/n = A007318(nk, k)/n = A060540(n, k)/A060540(n-1, k). EXAMPLE row 1: (2*n+1)/1! row 2: (3*n+1)*(3*n+2)/2! row 3: (4*n+1)*(4*n+2)*(4*n+3)/3! row 4: (5*n+1)*(5*n+2)*(5*n+3)*(5*n+4)/4! row 5: (6*n+1)*(6*n+2)*(6*n+3)*(6*n+4)*(6*n+5)/5!. Table begins: 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,... 1,3,5,7,9,11,13,15,17,19,21,23,25,27,... 1,10,28,55,91,136,190,253,325,406,496,... 1,35,165,455,969,1771,2925,4495,6545,... 1,126,1001,3876,10626,23751,46376,82251,... 1,462,6188,33649,118755,324632,749398,... 1,1716,38760,296010,1344904,4496388,... PROG (PARI) T(n, k)=binomial(n+n*k+k, n*k+k) (PARI) { i=0; write("b060543.txt", "0 1"); for (m=0, 20, for (k=0, m + 1, n=m - k + 1; write("b060543.txt", i++, " ", binomial(n + n*k + k, n*k + k))); ) } \\ Harry J. Smith, Jul 06 2009 CROSSREFS Cf. A108290, A108267, A108288, A108289, A060544 (row 2), A015219 (row 3). Rows include A000012, A001700, A025174. Columns include A000012, A005408, A060544. Main diagonal is A060545. Sequence in context: A106268 A267655 A263864 * A267751 A185996 A261215 Adjacent sequences:  A060540 A060541 A060542 * A060544 A060545 A060546 KEYWORD nonn,tabl AUTHOR Henry Bottomley, Apr 02 2001 EXTENSIONS Entry revised by Paul D. Hanna, May 31 2005 Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jun 17 2007 STATUS approved

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Last modified February 20 14:03 EST 2020. Contains 332078 sequences. (Running on oeis4.)