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A371028 a(n) = Sum_{k=1..n} (n + k - 1)! / (k!*(n - k)!) if n > 0 and a(0) = 1. Row sums of A370983.

%I A371028 #3 Mar 09 2024 04:38:10
%S A371028 1,1,5,35,364,5189,94471,2095015,54793880,1651345449,56350158193,
%T A371028 2147652456971,90423282500420,4168099478767405,208774492598428979,
%U A371028 11291105341823941327,655760745772682537776,40705101569058847374545,2689347796601389962641085,188430347768069305315294579
%N A371028 a(n) = Sum_{k=1..n} (n + k - 1)! / (k!*(n - k)!) if n > 0 and a(0) = 1. Row sums of A370983.
%p A371028 a := n -> local k; if n = 0 then 1 else add((n + k - 1)! / (k!*(n - k)!), k = 1..n) fi: seq(a(n), n = 0..19);
%Y A371028 Cf. A370983.
%K A371028 nonn
%O A371028 0,3
%A A371028 _Peter Luschny_, Mar 09 2024