This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A061355 #55 Apr 05 2025 04:56:22
%S A061355 1,1,2,3,24,60,720,252,40320,36288,3628800,4989600,95800320,
%T A061355 3113510400,17435658240,326918592000,20922789888000,2736057139200,
%U A061355 6402373705728000,30411275102208,2432902008176640000,25545471085854720000,224800145555521536000
%N A061355 Denominator of Sum_{k=0..n} 1/k!.
%C A061355 An inverse of A002034: A002034(a(n)) = n for n > 0. But not the least inverse: a(n) > A046021(n) for n > 3. - _Jonathan Sondow_, Jan 09 2005
%H A061355 Harry J. Smith, <a href="/A061355/b061355.txt">Table of n, a(n) for n = 0..200</a>
%H A061355 J. Sondow, <a href="http://arxiv.org/abs/0704.1282">A geometric proof that e is irrational and a new measure of its irrationality</a>, arXiv:0704.1282 [math.HO], 2007-2010.
%H A061355 J. Sondow, <a href="http://www.jstor.org/stable/27642006">A geometric proof that e is irrational and a new measure of its irrationality</a>, Amer. Math. Monthly 113 (2006) 637-641.
%H A061355 J. Sondow and K. Schalm, <a href="http://arxiv.org/abs/0709.0671">Which partial sums of the Taylor series for e are convergents to e? (and a link to the primes 2, 5, 13, 37, 463), II</a>, arXiv:0709.0671 [math.NT], 2007-2009; Gems in Experimental Mathematics (T. Amdeberhan, L. A. Medina, and V. H. Moll, eds.), Contemporary Mathematics, vol. 517, Amer. Math. Soc., Providence, RI, 2010.
%H A061355 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers.</a>
%F A061355 Denominators of floor(n!*exp(1))/n!. Denominators of coefficients in expansion of exp(x)/(1-x). - _Vladeta Jovovic_, Aug 11 2002
%F A061355 a(n) = n!/gcd(n!, 1 + n + n(n-1) + n(n-1)(n-2) + ... + n!). - _Jonathan Sondow_, Jan 09 2005
%F A061355 a(n) = denominator(exp(1)*gamma(n + 1,1)/gamma(n + 1)). - _Gerry Martens_, May 31 2018
%e A061355 1, 2, 5/2, 8/3, 65/24, 163/60, 1957/720, 685/252, ...
%p A061355 BB:=n->sum(1/i!, i=1..n): a:=n->floor(denom(BB(n))): seq(a(n), n=0..22); # _Zerinvary Lajos_, Mar 28 2007
%t A061355 A061355[n_] := Denominator[Sum[1/k!, {k, 0, n}]]; Array[A061355, 23, 0] (* _JungHwan Min_, Nov 08 2016 *)
%t A061355 Accumulate[1/Range[0,30]!]//Denominator (* _Harvey P. Dale_, Mar 24 2025 *)
%o A061355 (PARI) { default(realprecision, 500); e=exp(1); for (n=0, 200, a=denominator(floor(n!*e)/n!); write("b061355.txt", n, " ", a) ) } \\ _Harry J. Smith_, Jul 21 2009
%o A061355 (PARI) first(n) = my(res = vector(n), s = 0, f = 1); for(i = 1, n, f *= i; s += 1/f; res[i] = denominator(s)); res \\ _David A. Corneth_, May 31 2018
%o A061355 (GAP) List(List([0..25],n->Sum([0..n],k->1/Factorial(k))),DenominatorRat); # _Muniru A Asiru_, Jun 01 2018
%Y A061355 Cf. A061354 (numerators), A093101.
%Y A061355 a(n) = n!/A093101(n) for n > 0. See also A002034, A046021.
%K A061355 nonn,frac
%O A061355 0,3
%A A061355 _Amarnath Murthy_, Apr 28 2001