A220180 - OEIS

%I #7 Jan 10 2025 18:53:36

%S 1,1,4,42,924,36300,2265960,206703840,25945444560,4287205253520,

%T 901822916010240,235245784759302240,74515547291697610560,

%U 28171404151229273014080,12529985068482904127064960,6476871523103017023955968000,3850268179365489288889549267200

%N E.g.f.: exp( Sum_{n>=1} (n+1)^(n-1) * x^n / n ).

%F a(n) = Sum_{k=1..n} (n-1)!/(n-k)! * (k+1)^(k-1) * a(n-k) for n>0 with a(0)=1.

%e E.g.f.: A(x) = 1 + x + 4*x^2/2! + 42*x^3/3! + 924*x^4/4! + 36300*x^5/5! +...

%e where

%e log(A(x)) = x + 3*x^2/2 + 16*x^3/3 + 125*x^4/4 + 1296*x^5/5 + 16807*x^6/6 +...+ (n+1)^(n-1)*x^n/n +...

%o (PARI) {a(n)=if(n==0,1,sum(k=1,n, (n-1)!/(n-k)! * (k+1)^(k-1) * a(n-k)))}

%o for(n=0,12,print1(a(n),", "))

%K nonn

%O 0,3

%A _Paul D. Hanna_, Dec 06 2012