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

Author

Paul Curtz, Mar 28 2010

Keywords

• nonn

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.

Crossrefs

Cf. A002689, A091137.

Programs

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 *)

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

Formula

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

Extensions

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

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