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A220180 E.g.f.: exp( Sum_{n>=1} (n+1)^(n-1) * x^n / n ). 0
1, 1, 4, 42, 924, 36300, 2265960, 206703840, 25945444560, 4287205253520, 901822916010240, 235245784759302240, 74515547291697610560, 28171404151229273014080, 12529985068482904127064960, 6476871523103017023955968000, 3850268179365489288889549267200 (list; graph; refs; listen; history; text; internal format)
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: A143990 A267616 A243809 * A134356 A156479 A111829

Adjacent sequences:  A220177 A220178 A220179 * A220181 A220182 A220183

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Dec 06 2012

STATUS

approved

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Last modified November 21 11:30 EST 2018. Contains 317447 sequences. (Running on oeis4.)