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 A127328 #13 Feb 08 2025 18:39:23
%S A127328 1,0,3,3,15,30,99,252,747,2064,5973,16995,49089,141414,409755,1188243,
%T A127328 3455811,10064952,29368377,85809681,251067645,735446106,2156695533,
%U A127328 6330729438,18600079221,54693760680,160951905819,473984678037,1396755865527,4118553190254
%N A127328 Inverse binomial transform of A026641; binomial transform of A127361.
%C A127328 Hankel transform is 3^n.
%H A127328 G. C. Greubel, <a href="/A127328/b127328.txt">Table of n, a(n) for n = 0..1000</a>
%F A127328 a(n) = Sum_{k=0..n} Sum_{j=0..k} (-1)^(n+j)*binomial(k+j, j)*binomial(n, k). - _G. C. Greubel_, Apr 30 2019
%F A127328 a(n) ~ 3^n / sqrt(3*Pi*n). - _Vaclav Kotesovec_, Jul 20 2019
%t A127328 a[n_]:= Sum[(-1)^n*Sum[(-1)^j*Binomial[k+j, j], {j,0,k}]*Binomial[n, k], {k, 0, n}]; Table[a[n], {n, 0, 30}] (* _G. C. Greubel_, Apr 30 2019 *)
%o A127328 (PARI) {a(n) = sum(k=0,n, sum(j=0,k, (-1)^(n+j)*binomial(k+j, j)* binomial(n, k)))}; \\ _G. C. Greubel_, Apr 30 2019
%o A127328 (Magma) [ (&+[ (&+[(-1)^(n+j)*Binomial(k+j, j)*Binomial(n, k): j in [0..k]]): k in [0..n]]) : n in [0..30]]; // _G. C. Greubel_, Apr 30 2019
%o A127328 (Sage) [sum(sum((-1)^(n+j)*binomial(k+j, j)*binomial(n, k) for j in (0..k)) for k in (0..n)) for n in (0..30)] # _G. C. Greubel_, Apr 30 2019
%o A127328 (GAP) List([0..30], n-> Sum([0..n], k-> Sum([0..k], j-> (-1)^(n+j)* Binomial(k+j, j)*Binomial(n,k)))); # _G. C. Greubel_, Apr 30 2019
%K A127328 nonn
%O A127328 0,3
%A A127328 _Philippe Deléham_, Mar 29 2007
%E A127328 Terms a(10) onward added by _G. C. Greubel_, Apr 30 2019