A129716 n! times partial sum of the sequence (1,Bernoulli numbers).

1, 2, 3, 10, 40, 196, 1176, 8352, 66816, 589248, 5892480, 67841280, 814095360, 9007096320, 126099348480, 3417110323200, 54673765171200, -1593137026252800, -28676466472550400, 6142121597716070400, 122842431954321408000, -24453765000305786880000

Offset: 0

Author

Paul Curtz, Jun 02 2007

Keywords

• sign

Examples

			The sequence of 1 followed by Bernoulli numbers is 1, 1, -1/2, 1/6,0, -1/30, 0, 1/42, .... (Cf. A027641, A027642). Its partial sums are 1, 2, 3/2, 5/3, 5/3, ... Multiplication by n! for n=0,1,2,3,... yields a(n).
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..300 (terms 0..25 from R. J. Mathar)

Programs

GAP

List([0..25], n-> Factorial(n)*(1 + Sum([0..n-1], j-> Bernoulli(j)) ) ); # G. C. Greubel, Dec 03 2019

Magma

[1] cat [Factorial(n)*(1 + (&+[Bernoulli(k): k in [0..n-1]]) ): n in [1..25]]; // G. C. Greubel, Dec 03 2019

Maple

A129716 := proc(n) n!*(1+add(bernoulli(i),i=0..n-1)); end: seq(A129716(n),n=0..40) ; # R. J. Mathar, Feb 20 2008

Mathematica

max = 21; Accumulate[ Table[ If[n == 0, 1, BernoulliB[n-1]], {n, 0, max}]]*Range[0, max]! (* Jean-François Alcover, Mar 04 2013 *)

PARI

vector(26, n, (n-1)!*(1 + sum(j=0,n-2, bernfrac(j))) ) \\ G. C. Greubel, Dec 03 2019

Sage

[factorial(n)*(1 + sum(bernoulli(k) for k in (0..n-1)) ) for n in (0..25)] # G. C. Greubel, Dec 03 2019

Formula

a(n) = n!*(1 + Sum_{i=0..n-1} Bernoulli(i)). - R. J. Mathar, Feb 20 2008

Extensions

More terms from R. J. Mathar, Feb 20 2008