A158886 a(n) = (n+1)^n * n! * C(1/(n+1), n).

1, 1, -2, 21, -504, 21505, -1432080, 137227545, -17893715840, 3047775608241, -657209398809600, 175036741783305325, -56436686113876992000, 21667473499647065000625, -9768377272589156352395264

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..230

Formula

a(n) = Product_{k=0..n-1} (1 - k*(n+1)) for n>0 with a(0)=1.

a(n) = Coefficient of x^n/n! in (1 + (n+1)*x)^(1/(n+1)).

a(n) ~ (-1)^(n+1) * sqrt(2*Pi) * exp(1-n) * n^(2*n-3/2). - Vaclav Kotesovec, Jun 28 2015

Example

a(1) = 1, a(2) = 1*(-2), a(3) = 1*(-3)*(-7), a(4) = 1*(-4)*(-9)*(-14).

Maple

seq( (n+1)^n*n!*binomial(1/(n+1), n), n=0..20); # G. C. Greubel, Mar 04 2020

Mathematica

Table[(n+1)^n n!Binomial[1/(n+1), n], {n, 0, 20}] (* Harvey P. Dale, Oct 17 2013 *)

Prog

(PARI) {a(n) = (n+1)^n * n! * binomial(1/(n+1), n)}
for(n=0, 20, print1(a(n), ", "))
(PARI) {a(n) = if(n==0, 1, prod(k=0, n-1, 1 - k*(n+1) ))}
for(n=0, 20, print1(a(n), ", "))
(PARI) {a(n) = n!*polcoeff( (1 + (n+1)*x +x*O(x^n))^(1/(n+1)), n)}
for(n=0, 20, print1(a(n), ", "))
(Magma) [1] cat [(&*[1-j*(n+1): j in [0..n-1]]): n in [1..20]]; // G. C. Greubel, Mar 04 2020
(Sage) [(n+1)^n*factorial(n)*binomial(1/(n+1), n) for n in (0..20)] # G. C. Greubel, Mar 04 2020

Crossrefs

Cf. A158887.

Sequence in context: A303867 A238696 A226057 * A092957 A356481 A171107

Adjacent sequences: A158883 A158884 A158885 * A158887 A158888 A158889

Keyword

sign

Author

Paul D. Hanna, May 01 2009

Status

approved