A372348 - OEIS

%I #6 Jun 23 2024 16:12:55

%S 1,1,2,7,40,329,3550,47755,777812,15048925,341018314,8946278015,

%T 268923178720,9176058440977,352386991982390,15115253160180019,

%U 719367763801641580,37767206102310829445,2176271214087106315042,137024328250953628940455,9388717924596833591237624

%N a(n) = Sum_{j=0..n} p(n - j, j) where p(n, x) = Sum_{k=0..n} k! * Lah(n, k) * x^k where Lah = A271703.

%p Lah := (n, k) -> ifelse(n = k, 1, binomial(n-1, k-1)*n!/k!):

%p p := n -> local k; add(k!*Lah(n, k)*x^k, k = 0..n):

%p a := n -> local j; add(subs(x=j, p(n - j)), j = 0..n):

%p seq((a(n)), n = 0..21);

%Y Cf. A271703.

%K nonn

%O 0,3

%A _Peter Luschny_, Apr 28 2024