cp's OEIS Frontend

A350297 Triangle read by rows: T(n,k) = n!*(n-1)^k/k!.

%I A350297 #50 Feb 19 2022 07:37:02
%S A350297 1,1,0,2,2,1,6,12,12,8,24,72,108,108,81,120,480,960,1280,1280,1024,
%T A350297 720,3600,9000,15000,18750,18750,15625,5040,30240,90720,181440,272160,
%U A350297 326592,326592,279936,40320,282240,987840,2304960,4033680,5647152,6588344,6588344,5764801
%N A350297 Triangle read by rows: T(n,k) = n!*(n-1)^k/k!.
%C A350297 Rows n >= 2 are coefficients in a double summation power series for the integral of x^(1/x), and the integral of its inverse function y^(y^(y^(y^(...)))). See A350358.
%F A350297 T(n, k) = binomial(n, k)*A350269(n, k). - _Peter Luschny_, Dec 25 2021
%F A350297 T(n+1, k) = A061711(n) * (n+1) / A350149(n, k). - _Robert B Fowler_, Jan 11 2022
%e A350297 Triangle T(n,k) begins:
%e A350297   -----------------------------------------------------------------
%e A350297    n\k     0      1      2       3       4       5       6       7
%e A350297   -----------------------------------------------------------------
%e A350297    0  |    1,
%e A350297    1  |    1,     0,
%e A350297    2  |    2,     2,     1,
%e A350297    3  |    6,    12,    12,      8,
%e A350297    4  |   24,    72,   108,    108,     81,
%e A350297    5  |  120,   480,   960,   1280,   1280,   1024,
%e A350297    6  |  720,  3600,  9000,  15000,  18750,  18750,  15625,
%e A350297    7  | 5040, 30240, 90720, 181440, 272160, 326592, 326592, 279936.
%e A350297   ...
%p A350297 T := (n, k) -> (n!/k!)*(n - 1)^k:
%p A350297 seq(seq(T(n, k), k = 0..n), n = 0..8); # _Peter Luschny_, Dec 24 2021
%t A350297 T[1, 0] := 1; T[n_, k_] := n!*(n - 1)^k/k!; Table[T[n, k], {n, 0, 8}, {k, 0, n}] // Flatten (* _Amiram Eldar_, Dec 24 2021 *)
%Y A350297 Cf. A000142 (first column), A062119 (second column), A065440 (main diagonal), A055897 (subdiagonal), A217701 (row sums).
%Y A350297 Cf. A350269, A350358.
%Y A350297 Cf. A061711, A350149.
%K A350297 easy,nonn,tabl
%O A350297 0,4
%A A350297 _Robert B Fowler_, Dec 23 2021