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.
%I A104507 #21 Jul 30 2025 00:59:25
%S A104507 1,0,-2,-3,2,15,19,-28,-134,-129,353,1254,791,-4238,-11818,-3123,
%T A104507 49162,110007,-17783,-554458,-996323,690932,6096792,8624747,-12287153,
%U A104507 -65419110,-69285296,178655307,684550946,483569751,-2354830741,-6970706252,-2324044054,29195280375,68793790705
%N A104507 Row sums of triangle A104505, which is equal to the right-hand side of the triangle A084610 of coefficients in (1+x-x^2)^n.
%F A104507 G.f.: (x/((1-x))+1/((-sqrt(5*x^2-2*x+1)+x+1))*x*(1-(5*x-1)/(sqrt(5*x^2-2*x+1)))). - _Vladimir Kruchinin_, Oct 04 2015
%F A104507 a(n) = Sum_{j=0..n/2}((-1)^j*binomial(n,j)*binomial(n-j-1,n-2*j)). - _Vladimir Kruchinin_, Oct 04 2015
%F A104507 From _Peter Bala_, Jul 24 2025: (Start)
%F A104507 a(n) = [x^n] (1 - x^2/(1 - x))^n. Cf. A246437.
%F A104507 The Gauss congruences hold: a(n*p^k) == a(n*p^(k-1)) (mod p^k) for all primes p and all positive integers n and k.
%F A104507 exp(Sum_{n >= 1} a(n)*x^n/n) = 1 - x^2 - x^3 + x^4 + 4*x^5 + ... is the g.f. of A108623.(End)
%t A104507 CoefficientList[Series[(x/((1 - x)) + 1/((-Sqrt[5 x^2 - 2 x + 1] + x + 1)) x (1 - (5 x - 1)/(Sqrt[5 x^2 - 2 x + 1]))), {x, 0, 40}], x] (* _Vincenzo Librandi_, Oct 05 2015 *)
%o A104507 (PARI) a(n)=sum(k=0,n,polcoeff((1+x-x^2)^n,n+k))
%o A104507 (Maxima)
%o A104507 a(n):=sum((-1)^j*binomial(n,j)*binomial(n-j-1,n-2*j),j,0,n/2); /* _Vladimir Kruchinin_, Oct 04 2015 */
%o A104507 (PARI) a(n) = sum(k=0, n/2, (-1)^k*binomial(n,k)*binomial(n-k-1,n-2*k));
%o A104507 vector(40, n, a(n-1)) \\ _Altug Alkan_, Oct 04 2015
%Y A104507 Cf. A104505, A1086223, A246437, A370616, A386548.
%K A104507 sign,easy
%O A104507 0,3
%A A104507 _Paul D. Hanna_, Mar 11 2005