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 A355004 #13 Mar 22 2025 20:43:27
%S A355004 1,3,43,1333,63321,4034341,321994723,30869387193,3454384526353,
%T A355004 441903886812721,63608031487665171,10174227287873082853,
%U A355004 1790258521269694523113,343669522619597368671933,71473405251333054552561091,16008271911444915765782477041,3841639137772270982094393928353
%N A355004 a(n) = Sum_{k=0..n} A271703(k + n, n), row sums of A355005.
%F A355004 a(n) = A187535(n) * hypergeom([1, -n], [1 - 2*n, -2*n], -1).
%F A355004 From _Vaclav Kotesovec_, Jun 15 2022: (Start)
%F A355004 Recurrence: (n-1)^2 * n * (64*n^4 - 464*n^3 + 1244*n^2 - 1475*n + 663)*a(n) = (n-1)*(2*n-3)*(512*n^6 - 3968*n^5 + 11872*n^4 - 17336*n^3 + 12880*n^2 - 4597*n + 617)*a(n-1) + (2048*n^7 - 19968*n^6 + 78912*n^5 - 163216*n^4 + 191140*n^3 - 128857*n^2 + 48842*n - 8937)*a(n-2) + 4*(2*n-5)*(2*n-3)*(64*n^4 - 208*n^3 + 236*n^2 - 123*n + 32)*a(n-3).
%F A355004 a(n) ~ 2^(4*n - 1/2) * n^(n - 1/2) / (sqrt(Pi) * exp(n)). (End)
%p A355004 L := (n, k) -> ifelse(n = k, 1, binomial(n-1, k-1)*n! / k!):
%p A355004 seq(add(L(n + k, n), k = 0..n), n = 0..16);
%t A355004 Table[Sum[Binomial[n + k, n]*FactorialPower[n + k - 1, k], {k, 0, n}], {n, 0, 20}] (* _Vaclav Kotesovec_, Jun 15 2022 *)
%Y A355004 Cf. A271703 (unsigned Lah), A355005, A187535.
%K A355004 nonn
%O A355004 0,2
%A A355004 _Peter Luschny_, Jun 15 2022