|
%I #34 Oct 26 2019 09:55:46
%S 1,0,1,0,0,1,0,2,0,1,0,0,10,0,1,0,6,12,28,0,1,0,0,198,84,60,0,1,0,20,
%T 560,2076,324,110,0,1,0,0,5020,14240,12060,924,182,0,1,0,70,20580,
%U 213460,146680,49170,2184,280,0,1,0,0,144774,1984584,3479700,922680,158418,4536,408,0,1
%N Square array A(n,k), n>=0, k>=0, read by antidiagonals, where A(n,k) is the constant term in the expansion of (Sum_{j=0..n} j*(x^j + x^(-j)))^k.
%H Seiichi Manyama, <a href="/A322549/b322549.txt">Antidiagonals n = 0..50, flattened</a>
%e Square array begins:
%e 1, 0, 0, 0, 0, 0, 0, ...
%e 1, 0, 2, 0, 6, 0, 20, ...
%e 1, 0, 10, 12, 198, 560, 5020, ...
%e 1, 0, 28, 84, 2076, 14240, 213460, ...
%e 1, 0, 60, 324, 12060, 146680, 3479700, ...
%e 1, 0, 110, 924, 49170, 922680, 32108060, ...
%e 1, 0, 182, 2184, 158418, 4226040, 203474180, ...
%t A[0, 0] = 1; A[n_, k_] := Coefficient[Expand[Sum[j * (x^j + x^(-j)), {j, 0, n}]^k], x, 0]; Table[A[n-k, k], {n, 0, 10}, {k, n, 0, -1}] // Flatten (* _Amiram Eldar_, Dec 16 2018 *)
%o (PARI) T(n,k) = my(t=sum(j=0, n, j*(x^j + x^(-j)))^k); polcoef(numerator(t), poldegree(denominator(t))); \\ _Michel Marcus_, Dec 17 2018
%Y Columns 0-5: A000012, A000004, A006331, A303916, A305167, A318119.
%Y Main diagonal gives A318793.
%Y Cf. A201552.
%K nonn,tabl
%O 0,8
%A _Seiichi Manyama_, Dec 15 2018
|
