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A394081
Triangle read by rows: T(n, k) = n^(n - k)*Gamma(k + 1, k + 1)*exp(k + 1).
2
1, 1, 3, 4, 6, 17, 27, 27, 51, 142, 256, 192, 272, 568, 1569, 3125, 1875, 2125, 3550, 7845, 21576, 46656, 23328, 22032, 30672, 56484, 129456, 355081, 823543, 352947, 285719, 340942, 538167, 1057224, 2485567, 6805296, 16777216, 6291456, 4456448, 4653056, 6426624, 11046912, 22725184, 54442368, 148869153
OFFSET
0,3
LINKS
Paolo Xausa, Table of n, a(n) for n = 0..11475 (rows 0..150 of triangle, flattened).
EXAMPLE
Triangle starts:
[0] 1;
[1] 1, 3;
[2] 4, 6, 17;
[3] 27, 27, 51, 142;
[4] 256, 192, 272, 568, 1569;
[5] 3125, 1875, 2125, 3550, 7845, 21576;
[6] 46656, 23328, 22032, 30672, 56484, 129456, 355081;
[7] 823543, 352947, 285719, 340942, 538167, 1057224, 2485567, 680529;
MATHEMATICA
A394081[n_, k_] := If[n == 0, 1, n^(n-k)*Gamma[k+1, k+1]*Exp[k+1]];
Table[A394081[n, k], {n, 0, 10}, {k, 0, n}] (* Paolo Xausa, Apr 10 2026 *)
PROG
(Python)
from mpmath import mp, gammainc, exp, nint
def T(n: int, k: int) -> int:
mp.dps = 50
if k == 0: return n**n
val = n ** (n - k) * gammainc(k + 1, k + 1) * exp(k + 1)
return int(nint(val))
for n in range(8): print([T(n, k) for k in range(n + 1)])
CROSSREFS
Cf. A000312, A001865, A392923 (row sums).
Sequence in context: A122849 A068573 A138577 * A298149 A136242 A066732
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Mar 16 2026
STATUS
approved