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.
Triangle begins as: 1; 1, 1; 1, 2, 1; 1, 3, 4, 1; 1, 4, 8, 9, 1; 1, 5, 13, 22, 23, 1; 1, 6, 19, 41, 64, 65, 1; 1, 7, 26, 67, 131, 196, 197, 1;
a096465 n k = a096465_tabl !! n !! k a096465_row n = a096465_tabl !! n a096465_tabl = map reverse a091491_tabl -- Reinhard Zumkeller, Jul 12 2012
A096465:= func< n,k | k eq n select 1 else (n-k)*(&+[Binomial(n+k-2*j, n-j)/(n+k-2*j): j in [0..k]]) >; [A096465(n,k): k in [0..n], n in [0..12]]; // G. C. Greubel, Apr 30 2021
A096465:= (n,k)-> `if`(k=n, 1, (n-k)*add(binomial(n+k-2*j, n-j)/(n+k-2*j), j=0..k)); seq(seq(A096465(n,k), k=0..n), n=0..12) # G. C. Greubel, Apr 30 2021
T[, 0]= 1; T[n, n_]= 1; T[n_, m_]:= T[n, m]= T[n-1, m] + T[n, m-1]; T[n_, m_] /; n < 0 || m > n = 0; Table[T[n, m], {n, 0, 12}, {m, 0, n}]//Flatten (* Jean-François Alcover, Dec 17 2012 *)
def A096465(n,k): return 1 if (k==n) else (n-k)*sum( binomial(n+k-2*j, n-j)/(n+k-2*j) for j in (0..k)) flatten([[A096465(n,k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Apr 30 2021
a:= func< n | n eq 0 select 1 else (1+(-1)^n)/2 + (&+[ (&+[ ((n-2*j)/(n-2*k))*Binomial(n-2*k, n-k-j) : k in [0..j]]) : j in [0..Floor((n-1)/2)]]) >; [a(n): n in [0..45]]; // G. C. Greubel, Apr 30 2021
a[, 0]=1; a[n, n_]=1; a[n_, m_]:= a[n, m] = a[n-1, m] + a[n, m-1]; a[n_, m_] /; n<0 || m>n = 0; Table[ Sum[a[n-m, m], {m,0,n}], {n,0,45}] (* Jean-François Alcover, Dec 17 2012 *) a[n_]:= a[n]= (1+(-1)^n)/2 + Sum[(n-2*j)*Binomial[n-2*k, n-k-j]/(n-2*k), {j,0,(n-1)/2}, {k,0,j}]; Table[a[n], {n,0,45}] (* G. C. Greubel, Apr 30 2021 *)
def a(n): return (1+(-1)^n)/2 + sum( sum( ((n-2*j)/(n-2*k))*binomial(n-2*k, n-k-j) for k in (0..j)) for j in (0..(n-1)//2)) [a(n) for n in (0..45)] # G. C. Greubel, Apr 30 2021
Comments