OFFSET
0,12
COMMENTS
Rows of the array have g.f. x/((1+k*x)*(1-(k+1)*x)). - Philippe Deléham, Nov 24 2013
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1275
FORMULA
EXAMPLE
Rows start:
0 1 1 1 1 1 1 1 1 1 ...
0 1 1 3 5 11 21 43 85 171 ...
0 1 1 7 13 55 133 463 1261 4039 ...
0 1 1 13 25 181 481 2653 8425 40261 ...
0 1 1 21 41 461 1281 10501 36121 246141 ...
0 1 1 31 61 991 2821 32551 117181 1093711 ...
0 1 1 43 85 1891 5461 84883 314245 3879331 ...
0 1 1 57 113 3305 9633 194713 734161 11638089 ...
...
MAPLE
seq(seq( ((k+1)^(n-k) - (-k)^(n-k))/(2*k+1), k=0..n), n=0..12); # G. C. Greubel, Jan 27 2020
MATHEMATICA
T[n_, k_]:= ((n + 1)^k - (-n)^k)/(2n + 1); Flatten[Join[{0}, Table[T[k, n- k], {n, 1, 15}, {k, 0, n}]]] (* Indranil Ghosh, Mar 27 2017 *)
PROG
(PARI)
for(n=0, 10, for(k=0, 9, print1(((n+1)^k-(-n)^k)/(2*n+1), ", "); ); print(); ) \\ Andrew Howroyd, Mar 26 2017
(Magma) [((k+1)^(n-k) - (-k)^(n-k))/(2*k+1): k in [0..n], n in [0..12]]; // G. C. Greubel, Jan 27 2020
(Sage)
def T(n, k): return ((n+1)^k - (-n)^k)/(2*n+1)
[[T(k, n-k) for k in (0..n)] for n in (0..12)] # G. C. Greubel, Jan 27 2020
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Henry Bottomley, Jun 06 2002
STATUS
approved