A174727 a(n) = A091137(n+1)/(n+1).

2, 6, 8, 180, 288, 10080, 17280, 453600, 806400, 47900160, 87091200, 217945728000, 402361344000, 2241727488000, 4184557977600, 2000741783040000, 3766102179840000, 2838385676206080000, 5377993912811520000, 1686001091666411520000, 3211430650793164800000, 423033001181754163200000

Offset

0,1

Comments

Previous name: Inverse Akiyama-Tanigawa algorithm. From a column instead of a row. Bernoulli case A164555/A027642. We start from column 1, 1/2, 1/3, 1/4, 1/5 = A000012/A000027. First row: 1) (unreduced) 1, 1/2, 5/12, 9/24, 251/720 = A002657/A091137 (Cauchy from Bernoulli) (*); 2) (reduced) 1, 1/2, 5/12, 3/8, 251/720 = A002208/A002209 (Stirling and Bernoulli). Unreduced second row: 1/2, 1/6, 1/8, 19/180, 27/288, 863/10080 = A141417(n+1)/a(n).

(*) Reference page 56 (first row) and page 36 (upper main diagonal). From J. C. Adams (and Bashforth) numerical integration. See A165313 and A147998. See A002206 logarithm numbers (Gregory).

References

P. Curtz, Intégration numérique des systèmes différentiels .. . Note 12, Centre de Calcul Scientifique de l'Armement, Arcueil, 1969.

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = A091137(n+1)/(n+1).

Mathematica

A091137[n_] := A091137[n] = Product[d, {d, Select[ Divisors[n] + 1, PrimeQ]}]*A091137[n-1]; A091137[0] = 1; a[n_] := A091137[n+1]/(n+1); Table[a[n], {n, 0, 18}] (* Jean-François Alcover_, Aug 14 2012 *)

Prog

(PARI) f(n) = my(r =1); forprime(p=2, n+1, r*=p^(n\(p-1))); r; \\ A091137
a(n) = f(n+1)/(n+1); \\ Michel Marcus, Jun 30 2019

Crossrefs

Cf. A002689, A091137.

Sequence in context: A279258 A120709 A002689 * A046728 A110984 A021792

Adjacent sequences: A174724 A174725 A174726 * A174728 A174729 A174730

Keyword

nonn

Author

Paul Curtz, Mar 28 2010

Extensions

Extended up to a(18) by Jean-François Alcover, Aug 14 2012

New name and more terms from Michel Marcus, Jun 30 2019

Status

approved