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).

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

Offset

0,8

Links

Table of n, a(n) for n=0..70.

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

Cf. A000004, A000012, A005408, A056109, A056578, A056579 (rows 1-6).

Cf. A057427, A000217, A000337, A014915, A014916, A014917, A014918, A014920 (columns 1-7).

Sequence in context: A165253 A336541 A317659 * A348210 A122935 A131198

Adjacent sequences: A059042 A059043 A059044 * A059046 A059047 A059048

Keyword

nonn,easy,tabl

Author

Henry Bottomley, Dec 18 2000

Status

approved