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Search: id:A060543
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| A060543 |
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Triangle, read by antidiagonals, where T(n,k) = C(n+n*k+k, n*k+k). |
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+0
10
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| 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; listen)
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OFFSET
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0,5
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COMMENT
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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).
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LINKS
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Harry J. Smith, Table of n, a(n) for n=0,...,252
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FORMULA
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a(n) = A060539(n, k)/n = A007318(nk, k)/n = A060540(n, k)/A060540(n-1, k)
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EXAMPLE
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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,...
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PROGRAM
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(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))); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 06 2009]
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CROSSREFS
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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: A045912 A158695 A106268 this_sequence A060540 A087647 A100265
Adjacent sequences: A060540 A060541 A060542 this_sequence A060544 A060545 A060546
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KEYWORD
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nonn,tabl
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Apr 02 2001
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EXTENSIONS
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Entry revised by Paul D. Hanna (pauldhanna(AT)juno.com), May 31 2005
Edited by N. J. A. Sloane (njas(AT)research.att.com) at the suggestion of Andrew Plewe, Jun 17 2007
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