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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
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
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
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