This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
b:= proc(n, i, t) option remember; `if`(n=0, 1, `if`(t*i
n, 0, b(n-i, i, t-1))))
end:
a:= n-> b(n*(n-1), n, 2*(n-1)):
seq(a(n), n=0..25); # Alois P. Heinz, May 15 2016
T[0,p_,m_]=1; T[k_,0,m_]=0; T[k_,p_,m_]:=T[k,p,m]=Sum[T[k+i,p-1,-i], {i,-m,-1}]; Table[T[n(n-1),2n-2,n], {n,40}] (* T. D. Noe, Dec 19 2006 *)
a039744(n) = polcoef(matpascal(3*n-1, x)[3*n-1, n+1], n*(n-1)); \\ Max Alekseyev, Jun 16 2023
def a039744(n): return gaussian_binomial(3*n-2, n)[n*(n-1)] # Max Alekseyev, Jun 16 2023
a(4)=6 because discriminant of quartic x^4+a*x^2+b*x+c is -4*a^3*b^2 - 27*b^4 + 16*a^4*c + 144*a*b^2*c - 128*a^2*c^2 + 256*c^3 that consists of 6 monomials (parts).
1, 1, seq(nops(expand(discrim(x^n + add(c[i]*x^i,i=0..n-2),x))),n=3..12); # Robert Israel, Aug 10 2015
ClearAll[f]; a = {1,1}; Do[k = 0; Do[If[n > s - 2, If[n > s - 1, k = k + x^n], k = k + f[n] x^n], {n, 0, s}]; m = Resultant[k, D[k, x], x]; AppendTo[a, Length[m]], {s, 3, 8}]; a (* fixed by Vaclav Kotesovec, Mar 20 2019 *)
Flatten[{1, 1, Table[Length[Discriminant[x^n + Sum[Subscript[c, k]*x^k, {k, 0, n-2}], x]], {n, 3, 8}]}] (* Vaclav Kotesovec, Mar 20 2019 *)
a(5)=6 because discriminant of quintic x^5+a*x^2+b*x+c is: -27*a^4*b^2 + 256*b^5 + 108*a^5*c - 1600*a*b^3*c + 2250*a^2*b*c^2 + 3125*c^4 that consists of 6 monomials (parts).
a = {1, 1}; Do[k = 0; Do[If[n > s - 3, If[(n > s - 1) && ((n > s - 2)), k = k + x^n], k = k + f[n] x^n], {n, 0, s}]; m = Resultant[k, D[k, x], x]; AppendTo[a, Length[m]], {s, 3, 9}]; a (* fixed by Vaclav Kotesovec, Mar 20 2019 *)
Flatten[{1, 1, Table[Length[Discriminant[x^n + Sum[Subscript[c, k]*x^k, {k, 0, n-3}], x]], {n, 3, 9}]}] (* Vaclav Kotesovec, Mar 20 2019 *)
a(5)=7 because discriminant of sextic x^6+a*x^2+b*x+c is -27*a^4*b^2 + 256*b^5 + 108*a^5*c - 1600*a*b^3*c + 2250*a^2*b*c^2 + 3125*c^4 that consists of 6 monomials (parts).
a = {1, 1, 1}; Do[k = 0; Do[If[n > s - 4, If[(n > s - 1) && (n > s - 2) && (n > s - 3), k = k + x^n], k = k + f[n] x^n], {n, 0, s}]; m = Resultant[k, D[k, x], x]; AppendTo[a, Length[m]], {s, 4, 10}]; a (* Artur Jasinski, fixed by Vaclav Kotesovec, Mar 20 2019 *)
Flatten[{1, 1, 1, Table[Length[Discriminant[x^n + Sum[Subscript[c, k]*x^k, {k, 0, n-4}], x]], {n, 4, 10}]}] (* Vaclav Kotesovec, Mar 20 2019 *)
Table[(2 n - 1)!/(2 (n - 1)^2), {n, 2, 20}]
A138897:=n->(2*n - 1)!/(n*(n - 1)): seq(A138897(n), n=2..20); # Wesley Ivan Hurt, Nov 25 2017
Table[(2 n - 1)!/(n (n - 1)), {n, 2, 20}]
a(n) = (2*n - 1)!/(n*(n - 1)); \\ Michel Marcus, Oct 28 2017
Table[(2 n - 1)!/((n - 1)(n - 2)), {n, 3, 20}] (* R. J. Mathar, Apr 30 2008 *)
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