A280780
Numerators of coefficients in asymptotic expansion of S_n (number of simple permutations, A111111).
Original entry on oeis.org
1, -4, 2, -40, -182, -7624, -202652, -14115088, -30800534, -16435427656, -1051314228316, -22675483971248, -6980651581556876, -283099764343781072, -163910651754113166328, -43009695328217994139936, -793529010007812171331166, -20144221762701827321778088, -274475989492312981198559876
Offset: 0
Coefficients are 1, -4, 2, -40/3, -182/3, -7624/15, -202652/45, -14115088/315, -30800534/63, -16435427656/2835, ...
-
seq(N) = {
my(f = serreverse(x*Ser(vector(N, n, n!))));
Vec(x* f'/f * exp(2 + (f-x)/(x*f)));
};
apply(numerator, seq(20)) \\ Gheorghe Coserea, Jan 22 2017
A280781
Denominators of coefficients in asymptotic expansion of S_n (number of simple permutations, A111111).
Original entry on oeis.org
1, 1, 1, 3, 3, 15, 45, 315, 63, 2835, 14175, 22275, 467775, 1216215, 42567525, 638512875, 638512875, 834978375, 558242685, 1856156927625, 713906510625, 17717861581875, 2143861251406875, 9861761756471625, 147926426347074375, 75472666503609375, 48076088562799171875
Offset: 0
Coefficients are 1, -4, 2, -40/3, -182/3, -7624/15, -202652/45, -14115088/315, -30800534/63, -16435427656/2835, ...
-
seq(N) = {
my(f = serreverse(x*Ser(vector(N, n, n!))));
Vec(x* f'/f * exp(2 + (f-x)/(x*f)));
};
apply(denominator, seq(28)) \\ Gheorghe Coserea, Jan 22 2017
A280778
Numerators of coefficients in asymptotic expansion of M_n (number of monolithic chord diagrams, A280775).
Original entry on oeis.org
1, -4, -6, -154, -1610, -34588, -4666292, -553625626, -1158735422, -388434091184, -31268175015478, -2796356409576766, -4624948938397276052, -1691272281281652408568, -2154089954877183990112, -170222948041126582837968646, -5761785676811885455064909606, -55629298859254851627617870836
Offset: 0
Coefficients are 1, -4, -6, -154/3, -1610/3, -34588/5, -4666292/45, -553625626/315, -1158735422/35, ...
-
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
A280779
Denominators of coefficients in asymptotic expansion of M_n (number of monolithic chord diagrams, A280775).
Original entry on oeis.org
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
Coefficients are 1, -4,-6, -154/3, -1610/3, -34588/5, -4666292/45, -553625626/315, -1158735422/35, ...
-
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
A280776
Numerators of coefficients in asymptotic expansion of C_n (number of connected chord diagrams, A000699).
Original entry on oeis.org
1, -5, -43, -579, -44477, -5326191, -180306541, -203331297947, -58726239094693, -781618285277957, -1025587838964854273, -35763822710356866613, -330773478104531041960421, -237504847171108896327033959, -196526060612842999084524774697, -20633624138373135772483762873819
Offset: 0
Coefficients are 1, -5/2, -43/8, -579/16, -44477/128, -5326191/1280, -180306541/3072, ...
-
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(C = 'x*Ser(A000699_seq(N))); Vec(x*exp(1-(2*C+C^2)/(2*x))/C);
apply(numerator, seq(16)) \\ Gheorghe Coserea, Jan 22 2017
Showing 1-5 of 5 results.
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