cp's OEIS Frontend

A362277 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = n! * Sum_{j=0..floor(n/2)} (-k/2)^j * binomial(n-j,j)/(n-j)!.

%I A362277 #26 Apr 16 2023 09:49:00
%S A362277 1,1,1,1,1,1,1,1,0,1,1,1,-1,-2,1,1,1,-2,-5,-2,1,1,1,-3,-8,1,6,1,1,1,
%T A362277 -4,-11,10,41,16,1,1,1,-5,-14,25,106,31,-20,1,1,1,-6,-17,46,201,-44,
%U A362277 -461,-132,1,1,1,-7,-20,73,326,-299,-1952,-895,28,1,1,1,-8,-23,106,481,-824,-5123,-1028,6481,1216,1
%N A362277 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = n! * Sum_{j=0..floor(n/2)} (-k/2)^j * binomial(n-j,j)/(n-j)!.
%H A362277 Seiichi Manyama, <a href="/A362277/b362277.txt">Antidiagonals n = 0..139, flattened</a>
%F A362277 E.g.f. of column k: exp(x - k*x^2/2).
%F A362277 T(n,k) = T(n-1,k) - k*(n-1)*T(n-2,k) for n > 1.
%F A362277 T(n,k) = n! * Sum_{j=0..floor(n/2)} (-k/2)^j / (j! * (n-2*j)!).
%e A362277 Square array begins:
%e A362277   1,  1,  1,   1,    1,    1,     1, ...
%e A362277   1,  1,  1,   1,    1,    1,     1, ...
%e A362277   1,  0, -1,  -2,   -3,   -4,    -5, ...
%e A362277   1, -2, -5,  -8,  -11,  -14,   -17, ...
%e A362277   1, -2,  1,  10,   25,   46,    73, ...
%e A362277   1,  6, 41, 106,  201,  326,   481, ...
%e A362277   1, 16, 31, -44, -299, -824, -1709, ...
%o A362277 (PARI) T(n,k) = n!*sum(j=0,n\2, (-k/2)^j/(j!*(n-2*j)!));
%Y A362277 Columns k=0..6 give A000012, (-1)^n * A001464(n), A293604, A362278, A362176, A362279, A362177.
%Y A362277 Main diagonal gives A362276.
%Y A362277 T(n,2*n) gives A362282.
%Y A362277 Cf. A359762, A362302.
%K A362277 sign,tabl
%O A362277 0,14
%A A362277 _Seiichi Manyama_, Apr 13 2023