A248592 -id:A248592 - cp's OEIS frontend

A280779 Denominators of coefficients in asymptotic expansion of M_n (number of monolithic chord diagrams, A280775).

1, 1, 1, 3, 3, 5, 45, 315, 35, 567, 2025, 7425, 467775, 6081075, 257985, 638512875, 638512875, 172297125, 13956067125, 74246277105, 3093594879375, 14992036723125, 2143861251406875, 16436269594119375, 4226469324202125, 48028060502296875, 593531957565421875, 56437147443285984375

Offset: 0

N. J. A. Sloane, Jan 19 2017

This has the same start as two other sequences, A241591 and A248592, but appears to be different from both.

			Coefficients are 1, -4,-6, -154/3, -1610/3, -34588/5, -4666292/45, -553625626/315, -1158735422/35, ...

Gheorghe Coserea, Table of n, a(n) for n = 0..101
Michael Borinsky, Generating asymptotics for factorially divergent sequences, arXiv preprint arXiv:1603.01236 [math.CO], 2016.

Cf. A000699, A280775, A111111, A280777, A280778, A280780, A280781.

Cf. also A241591, A248592.

A000699_seq(N) = {
  my(a = vector(N)); a[1] = 1;
  for (n=2, N, a[n] = sum(k=1, n-1, (2*k-1)*a[k]*a[n-k])); a;
};
seq(N) = {
  my(M = subst(x*Ser(A000699_seq(N)), x, x/(1-x)^2));
  Vec(x/(1-x)*exp(1-x/2-(1-x)^2/(2*x)*(2*M + M^2))/M);
};
apply(numerator, seq(18))  \\ Gheorghe Coserea, Jan 22 2017

A241591 Denominators of Postnikov's hook-length formula 2^n*(n+1)^(n-1)/n!.

Original entry on oeis.org

1, 1, 1, 3, 3, 5, 45, 315, 35, 567, 14175, 1925, 467775, 868725, 7007, 638512875, 638512875, 14889875, 97692469875, 14849255421, 28868125, 17717861581875, 2143861251406875, 2505147019375, 236682282155319, 284473896821296875, 814172781296875, 3784415134680984375

Offset: 0

N. J. A. Sloane, May 13 2014

			1, 2, 6, 64/3, 250/3, 1728/5, 67228/45, 2097152/315, 1062882/35, 80000000/567, 9431790764/14175, 6115295232/1925, 7168641576148/467775, ...

Alexander Postnikov. Permutohedra, associahedra, and beyond. in: Conference in Honor of Richard Stanley's Sixtieth Birthday, June 2004. International Mathematics Research Notices, 6:1026-1106, 2009.

Matthew Wilson, Bruhat order on fixed-point-free involutions in the symmetric group, Electron. J. Combin., 21(2) (2014), #P2.20.

Cf. A241590.

Has same start as A248592 but is a different sequence.

t1:= [seq(2^n*(n+1)^(n-1)/n!,n=0..50)]:
t2:=map(numer, t1); # A241590
t3:=map(denom, t1); # A241591

vector(30, n, n--; denominator(2^n*(n+1)^(n-1)/n!)) \\ Michel Marcus, Jul 18 2015

A248591 Numerators of the (simplified) rationals n*2^(n - 1)/(n - 1)! .

Original entry on oeis.org

1, 4, 6, 16, 10, 8, 28, 64, 2, 8, 44, 32, 52, 16, 8, 256, 34, 8, 76, 32, 4, 16, 184, 128, 4, 16, 8, 64, 232, 32, 496, 1024, 2, 8, 4, 32, 148, 16, 8, 128, 164, 16, 344, 64, 8, 32, 752, 512, 4, 16, 8, 64, 424, 32, 16, 256, 8, 32, 944, 128, 976, 64, 32, 4096, 2

Offset: 1

James Burling, Oct 09 2014

James Burling, Another Special Rational Sequence

Cf. A248592 (denominators).

[Numerator(n*2^(n-1)/Factorial(n-1)): n in [1..70]]; // Vincenzo Librandi, Oct 16 2014

Table[Numerator[n 2^(n - 1)/(n - 1)!], {n, 1, 70}] (* Vincenzo Librandi, Oct 16 2014 *)

vector(100, n, numerator(n*2^(n - 1)/(n - 1)!)) \\ Michel Marcus, Oct 09 2014

a(n) = numerator(n*2^(n - 1)/(n - 1)!).

a(n) = numerator(g(1, n)) where g(m, n) = m if m = n; 2*g(m + 1, n)/m otherwise.

More terms from Michel Marcus, Oct 09 2014

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A280779 Denominators of coefficients in asymptotic expansion of M_n (number of monolithic chord diagrams, A280775).

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A241591 Denominators of Postnikov's hook-length formula 2^n*(n+1)^(n-1)/n!.

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A248591 Numerators of the (simplified) rationals n*2^(n - 1)/(n - 1)! .

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