OFFSET
0,5
REFERENCES
A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1325
FORMULA
A(n,k) = (1 + k*n)*binomial(2*n,n)/(n+1).
A(n,k) = 2*(k*n+1)*(2*n-1)*A(n-1,k)/((n+1)*(k*n-k+1)) for n > 0.
G.f. of column k: (k - 1 - (2*k-4)*x - (k-1)*sqrt(1 - 4*x))/(2*x*sqrt(1 - 4*x)).
EXAMPLE
Array begins:
====================================================
n\k | 0 1 2 3 4 5 6 7
----+-----------------------------------------------
0 | 1 1 1 1 1 1 1 1 ...
1 | 1 2 3 4 5 6 7 8 ...
2 | 2 6 10 14 18 22 26 30 ...
3 | 5 20 35 50 65 80 95 110 ...
4 | 14 70 126 182 238 294 350 406 ...
5 | 42 252 462 672 882 1092 1302 1512 ...
6 | 132 924 1716 2508 3300 4092 4884 5676 ...
7 | 429 3432 6435 9438 12441 15444 18447 21450 ...
...
PROG
(PARI) T(n, k)={(1 + k*n)*binomial(2*n, n)/(n+1)}
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Jan 04 2020
STATUS
approved