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A002688 Denominators of coefficients for repeated integration.
(Formerly M4158 N1728)
1

%I M4158 N1728

%S 6,24,45,480,10080,24192,907200,1036800,239500800,106444800,

%T 9906624000,475517952000,15692092416000,4828336128000,

%U 8002967132160000,4268249137152000,51607012294656000,1202139815804928000

%N Denominators of coefficients for repeated integration.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H H. E. Salzer, <a href="http://dx.doi.org/10.1080/14786444708521604">Table of coefficients for repeated integration with differences</a>, Phil. Mag., 38 (1947), 331-336.

%H H. E. Salzer, <a href="/A002206/a002206_1.pdf">Table of coefficients for repeated integration with differences</a>, Phil. Mag., 38 (1947), 331-336. [Annotated scanned copy]

%F a(n) = denominator(1/n!*(Sum_{k=1..n}((stirling1(n,k))/((k+1)*(k+2))))). - _Vladimir Kruchinin_, Apr 06 2016

%p seq(denom(int(int(mul(p-i,i=0..(n-1)),p=0..p),p=0..1)/n!),n=1..30); # Herman Jamke (hermanjamke(AT)fastmail.fm), Aug 01 2010

%t Table[Denominator@ (Sum[StirlingS1[n, k]/((k + 1) (k + 2)), {k, n}]/n!), {n, 20}] (* _Michael De Vlieger_, Apr 06 2016 *)

%o (Maxima)

%o a(n):=denom(1/n!*(sum((stirling1(n,k))/((k+1)*(k+2)),k,1,n))); /* _Vladimir Kruchinin_, Apr 06 2016 */

%Y Cf. A002687.

%K nonn,frac

%O 1,1

%A _N. J. A. Sloane_.

%E More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Aug 01 2010

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Last modified April 20 03:36 EDT 2019. Contains 322294 sequences. (Running on oeis4.)