A220180 E.g.f.: exp( Sum_{n>=1} (n+1)^(n-1) * x^n / n ).

1, 1, 4, 42, 924, 36300, 2265960, 206703840, 25945444560, 4287205253520, 901822916010240, 235245784759302240, 74515547291697610560, 28171404151229273014080, 12529985068482904127064960, 6476871523103017023955968000, 3850268179365489288889549267200

Offset

0,3

Links

Table of n, a(n) for n=0..16.

Formula

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

Example

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

Prog

(PARI) {a(n)=if(n==0, 1, sum(k=1, n, (n-1)!/(n-k)! * (k+1)^(k-1) * a(n-k)))}
for(n=0, 12, print1(a(n), ", "))

Crossrefs

Sequence in context: A352074 A267616 A243809 * A134356 A156479 A355130

Adjacent sequences: A220177 A220178 A220179 * A220181 A220182 A220183

Keyword

nonn

Author

Paul D. Hanna, Dec 06 2012

Status

approved