OFFSET
0,5
COMMENTS
FORMULA
See formulas at A274390, which is the main entry for this table.
EXAMPLE
See examples at A274390, which is the main entry for this table.
This table begins:
1, 0, 0, 0, 0, 0, 0, ...;
1, 2, 9, 64, 625, 7776, 117649, ...;
1, 4, 30, 332, 4880, 89742, 1986124, ...;
1, 6, 63, 948, 18645, 454158, 13221075, ...;
1, 8, 108, 2056, 50680, 1537524, 55494712, ...;
1, 10, 165, 3800, 112625, 4090980, 176238685, ...;
1, 12, 234, 6324, 219000, 9266706, 463975764, ...;
1, 14, 315, 9772, 387205, 18704322, 1067280319, ...;
1, 16, 408, 14288, 637520, 34617288, 2217367600, ...;
...
This table may also be written as a triangle:
1;
0, 1;
0, 2, 1;
0, 9, 4, 1;
0, 64, 30, 6, 1;
0, 625, 332, 63, 8, 1;
0, 7776, 4880, 948, 108, 10, 1;
0, 117649, 89742, 18645, 2056, 165, 12, 1;
0, 2097152, 1986124, 454158, 50680, 3800, 234, 14, 1;
0, 43046721, 51471800, 13221075, 1537524, 112625, 6324, 315, 16, 1;
0, 1000000000, 1530489744, 448434136, 55494712, 4090980, 219000, 9772, 408, 18, 1, 0;
...
PROG
(PARI) {ITERATE(F, n, k) = my(G=x +x*O(x^k)); for(i=1, n, G=subst(G, x, F)); G}
{T(n, k) = my(TREE = serreverse(x*exp(-x +x*O(x^k)))); k!*polcoeff(ITERATE(TREE, n, k), k)}
/* Print this table as a rectangular array */
for(n=0, 10, for(k=1, 10, print1(T(n, k), ", ")); print(""))
/* Print this table as a triangle */
for(n=1, 12, for(k=0, n-1, print1(T(k, n-k), ", ")); print("") )
/* Print this table as a flattened array */
for(n=0, 12, for(k=0, n-1, print1(T(k, n-k), ", ")); )
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Paul D. Hanna, Jul 04 2016
STATUS
approved