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A158887 a(n) = (n+1)^n * n! * binomial(n-1 + 1/(n+1), n). 3
1, 1, 4, 45, 1056, 43225, 2756160, 253586025, 31872332800, 5252921480961, 1099886703552000, 285322741626047125, 89844523369696972800, 33764841634845724313625, 14930493174337400252809216 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
a(n) = Product_{k=0..n-1} (k*(n+1) + 1) for n>0 with a(0)=1.
a(n) = coefficient of x^n/(n!*(n+1)^n) in 1/(1-x)^(1/(n+1)).
a(n) ~ sqrt(2*Pi) * exp(1-n) * n^(2*n-3/2). - Vaclav Kotesovec, Jun 28 2015
a(n) = (1+n)^n * gamma(n+1/(n+1)) / gamma(1/(n+1)). - Gerry Martens, May 30 2018
EXAMPLE
a(1) = 1, a(2) = 1*4, a(3) = 1*5*9, a(4) = 1*6*11*16, a(5) = 1*7*13*19*25.
MAPLE
seq(mul(j*(n+1)+1, j=0..n-1), n = 0..15); # G. C. Greubel, Mar 04 2020
MATHEMATICA
Table[(n+1)^n n!Binomial[n-1+1/(n+1), n], {n, 0, 20}] (* Harvey P. Dale, Oct 26 2011 *)
a[n_] := (1 + n)^n Gamma[n + 1/(1 + n)]/Gamma[1/(n + 1)] // FullSimplify
Table[a[n], {n, 0, 20} (* Gerry Martens, May 30 2018 *)
PROG
(PARI) a(n)=(n+1)^n*n!*polcoeff(1/(1-x+x*O(x^n))^(1/(n+1)), n)
(PARI) a(n)=if(n==0, 1, prod(k=0, n-1, k*(n+1)+1))
(Magma) [1] cat [&*[j*(n+1)+1: j in [0..n-1]]: n in [1..15]]; // G. C. Greubel, Mar 04 2020
(Sage) [product(j*(n+1)+1 for j in (0..n-1)) for n in (0..15)] # G. C. Greubel, Mar 04 2020
(GAP) List([0..15], n-> Product([0..n-1], j-> j*(n+1)+1) ); # G. C. Greubel, Mar 04 2020
CROSSREFS
Sequence in context: A338456 A276292 A174484 * A126452 A082765 A132873
KEYWORD
nonn
AUTHOR
Paul D. Hanna, May 01 2009
STATUS
approved

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Last modified May 20 02:30 EDT 2024. Contains 372703 sequences. (Running on oeis4.)