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A059045 Square array T(n,k) read by antidiagonals where T(0,k) = 0 and T(n,k) = 1 + 2k + 3k^2 + ... + n*k^(n-1). 4
0, 1, 0, 1, 1, 0, 1, 3, 1, 0, 1, 6, 5, 1, 0, 1, 10, 17, 7, 1, 0, 1, 15, 49, 34, 9, 1, 0, 1, 21, 129, 142, 57, 11, 1, 0, 1, 28, 321, 547, 313, 86, 13, 1, 0, 1, 36, 769, 2005, 1593, 586, 121, 15, 1, 0, 1, 45, 1793, 7108, 7737, 3711, 985, 162, 17, 1, 0, 1, 55, 4097, 24604, 36409 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,8
LINKS
FORMULA
T(n,k) = n*k^(n-1)+T(n-1, k) = (n*k^(n+1)-(n+1)*k^n+1)/(k-1)^2.
EXAMPLE
0, 0, 0, 0, 0, 0, 0, 0, 0, ...
1, 1, 1, 1, 1, 1, 1, 1, 1, ...
1, 3, 5, 7, 9, 11, 13, 15, 17, ...
1, 6, 17, 34, 57, 86, 121, 162, 209, ...
1, 10, 49, 142, 313, 586, 985, 1534, 2257, ...
1, 15, 129, 547, 1593, 3711, 7465, 13539, 22737, ...
1, 21, 321, 2005, 7737, 22461, 54121, 114381, 219345, ...
1, 28, 769, 7108, 36409, 131836, 380713, 937924, 2054353, ...
MAPLE
A059045 := proc(n, k)
if k = 1 then
n*(n+1) /2 ;
else
(1+n*k^(n+1)-k^n*(n+1))/(k-1)^2 ;
end if;
end proc: # R. J. Mathar, Mar 29 2013
CROSSREFS
Sequence in context: A165253 A336541 A317659 * A348210 A122935 A131198
KEYWORD
nonn,easy,tabl
AUTHOR
Henry Bottomley, Dec 18 2000
STATUS
approved

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Last modified March 28 15:58 EDT 2024. Contains 371254 sequences. (Running on oeis4.)