A274740 - OEIS

A274740

Table of coefficients in the iterations of Euler's tree function (A000169), as read by antidiagonals.

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, 25937424601, 51395228090, 17386204761, 2325685632, 176238685, 9266706, 387205, 14288, 513, 20, 1

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,5

COMMENTS

See examples and formulas at A274390, which is the main entry for this table.

This entry is the same as table A274390, but read by antidiagonals from top down.

LINKS

Table of n, a(n) for n=0..77.

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:

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

Cf. A274390.

Sequence in context: A338858 A201897 A246658 * A360657 A327350 A137452

Adjacent sequences: A274737 A274738 A274739 * A274741 A274742 A274743

KEYWORD

nonn,tabl

AUTHOR

Paul D. Hanna, Jul 04 2016

STATUS

approved