cp's OEIS Frontend

A247504 Square array read by antidiagonals, A(n,k) = k!*[x^k]((1-Sum_{j=1..n} x^j)^(-1)), (n>=0,k>=0).

%I A247504 #9 Mar 27 2018 16:24:58
%S A247504 1,1,0,1,1,0,1,1,2,0,1,1,4,6,0,1,1,4,18,24,0,1,1,4,24,120,120,0,1,1,4,
%T A247504 24,168,960,720,0,1,1,4,24,192,1560,9360,5040,0,1,1,4,24,192,1800,
%U A247504 17280,105840,40320,0,1,1,4,24,192,1920,20880,221760,1370880,362880,0
%N A247504 Square array read by antidiagonals, A(n,k) = k!*[x^k]((1-Sum_{j=1..n} x^j)^(-1)), (n>=0,k>=0).
%e A247504 n\k[0][1][2] [3]  [4]   [5]    [6]     [7]      [8]       [9]
%e A247504 [0] 1, 0, 0,  0,   0,    0,     0,      0,       0,        0
%e A247504 [1] 1, 1, 2,  6,  24,  120,   720,   5040,   40320,   362880 [A000142]
%e A247504 [2] 1, 1, 4, 18, 120,  960,  9360, 105840, 1370880, 19958400 [A005442]
%e A247504 [3] 1, 1, 4, 24, 168, 1560, 17280, 221760, 3265920, 54069120
%e A247504 [.] .  .  .  .  .   .   .   .    .    .    .     .     .
%e A247504 oo] 1, 1, 4, 24, 192, 1920, 23040, 322560, 5160960, 92897280 [A002866]
%e A247504 '
%e A247504 As a triangular array, starts:
%e A247504 1,
%e A247504 1, 0,
%e A247504 1, 1, 0,
%e A247504 1, 1, 2, 0,
%e A247504 1, 1, 4, 6,  0,
%e A247504 1, 1, 4, 18, 24,  0,
%e A247504 1, 1, 4, 24, 120, 120, 0,
%e A247504 1, 1, 4, 24, 168, 960, 720, 0.
%p A247504 A := (n,k) -> k!*coeff(series((1-add(x^j, j=1..n))^(-1),x,k+2),x,k): seq(print(seq(A(n,k), k=0..9)), n=0..7);
%Y A247504 Cf. A247505, A247506, A002866, A000142, A005442.
%K A247504 nonn,tabl
%O A247504 0,9
%A A247504 _Peter Luschny_, Nov 03 2014