A241591 -id:A241591 - 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

A248592 Denominators of the (simplified) rational numbers n*2^(n - 1)/(n - 1)! .

Original entry on oeis.org

1, 1, 1, 3, 3, 5, 45, 315, 35, 567, 14175, 51975, 467775, 868725, 2837835, 638512875, 638512875, 1206079875, 97692469875, 371231385525, 441942125625, 17717861581875, 2143861251406875, 16436269594119375, 5917057053882975, 284473896821296875, 1780595872696265625

Offset: 1

James Burling, Oct 09 2014

James Burling, Another Special Rational Sequence

Cf. A248591 (numerators).

Has same start as A241591 but is a different sequence.

A248592 := proc(n)
    n*2^(n-1)/(n-1)! ;
    denom(%) ;
end proc:
seq(A248592(n),n=1..30) ; # R. J. Mathar, Oct 10 2014

vector(40, n, denominator(n*2^(n - 1)/(n - 1)!)) \\ Michel Marcus, Oct 09 2014

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

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

More terms from Michel Marcus, Oct 09 2014

A241590 Numerators of Postnikov's hook-length formula 2^n*(n+1)^(n-1)/n!.

Original entry on oeis.org

1, 2, 6, 64, 250, 1728, 67228, 2097152, 1062882, 80000000, 9431790764, 6115295232, 7168641576148, 64793042714624, 2562890625000, 1152921504606846976, 5724846103019631586, 666334875701477376, 21921547431139208743756, 16777216000000000000000, 164839190645167033716, 513039635408293850333052928

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. A241591.

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

Join[{1},Table[(2^n (n+1)^(n-1))/n!,{n,30}]//Numerator] (* Harvey P. Dale, Feb 23 2023 *)

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

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

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A248592 Denominators of the (simplified) rational numbers n*2^(n - 1)/(n - 1)! .

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A241590 Numerators of Postnikov's hook-length formula 2^n*(n+1)^(n-1)/n!.

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