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A306625
Regular triangle T(n,k) = binomial(2*n-2*k,n-k)*((n+1)/k)*Sum_{k=0..floor((k-1)/2)} (-1)^k*binomial(2*k,k)*binomial(n+3*k-2*k,k-2*k-1), read by rows.
0
2, 6, 12, 24, 36, 80, 100, 150, 240, 560, 420, 660, 1020, 1680, 4032, 1764, 2940, 4620, 7224, 12096, 29568, 7392, 13104, 21280, 33320, 52416, 88704, 219648, 30888, 58212, 98280, 156870, 244800, 386496, 658944, 1647360, 128700, 257400, 452760, 742140, 1170540, 1821600, 2882880, 4942080, 12446720
OFFSET
1,1
LINKS
R. T. Eakin, A combinatorial partition of Mersenne numbers arising from spectroscopy, Journal of Number Theory, Volume 132, Issue 10, October 2012, Pages 2166-2183.
EXAMPLE
Triangle begins
2,
6, 12,
24, 36, 80,
100, 150, 240, 560,
420, 660, 1020, 1680, 4032,
1764, 2940, 4620, 7224, 12096, 29568,
...
PROG
(PARI) T(n, r) = binomial(2*n-2*r, n-r)*((n+1)/r)*sum(k=0, (r-1)\2, (-1)^k*binomial(2*r, k)*binomial(n+3*r-2*k, r-2*k-1));
tabl(nn) = for (n=1, nn, for (k=1, n, print1(T(n, k), ", ")); );
CROSSREFS
Sum of n-th row equals A000984(n)*A000225(n).
Right diagonal is A069723 starting at index 2.
Sequence in context: A067718 A210594 A307252 * A262986 A307559 A211978
KEYWORD
nonn,tabl
AUTHOR
Michel Marcus, Mar 01 2019
STATUS
approved