A318124 -id:A318124 - cp's OEIS frontend

A318125 a(n) = [x^n] exp(Sum_{k>=1} (-1)^(k+1)x^k(1 + (n - 3)x^k)/(k(1 - x^k)^4)).

1, 1, 3, 14, 54, 238, 1026, 4573, 20404, 91902, 415953, 1891908, 8638846, 39569655, 181766878, 836950153, 3861927937, 17853107055, 82668539290, 383360628369, 1780126898575, 8275908734103, 38517137597486, 179442212204245, 836741558761935, 3905012142470483

Offset: 0

Ilya Gutkovskiy, Aug 18 2018

nonn

For n > 2, a(n) is the n-th term of the weigh transform of n-gonal pyramidal numbers.

N. J. A. Sloane, Transforms
Index to sequences related to pyramidal numbers

Cf. A258343, A281156, A294842, A294843, A294844, A294845, A318121, A318124.

Table[SeriesCoefficient[Exp[Sum[(-1)^(k + 1) x^k (1 + (n - 3) x^k)/(k (1 - x^k)^4), {k, 1, n}]], {x, 0, n}], {n, 0, 25}]

a(n) ~ c * d^n / sqrt(n), where d = 4.761510955746025663058811... and c = 0.2241869836397882024713... - Vaclav Kotesovec, Aug 19 2018

A320254 a(n) = n! * [x^n] exp(exp(x)(x + (n/2 - 1)x^2)).

Original entry on oeis.org

1, 1, 3, 16, 125, 1291, 16177, 241207, 4153193, 81082225, 1770989921, 42763506919, 1131353484637, 32541516492811, 1011058416700529, 33745374949198231, 1204107124715441873, 45741398365345761073, 1843069565594762478145, 78511973999963036415967, 3525468554804288803649381

Offset: 0

Ilya Gutkovskiy, Oct 08 2018

nonn

For n > 2, a(n) is the n-th term of the exponential transform of n-gonal numbers.

N. J. A. Sloane, Transforms
Index to sequences related to polygonal numbers

Cf. A000248, A033462, A279361, A279644, A318118, A318124, A320255.

Table[n! SeriesCoefficient[Exp[Exp[x] (x + (n/2 - 1) x^2)], {x, 0, n}], {n, 0, 20}]

A320255 a(n) = n! * [x^n] log(1 + exp(x)(x + (n/2 - 1)x^2)).

Original entry on oeis.org

0, 1, 1, -1, -26, 39, 3666, -7400, -1488416, 3802113, 1322570530, -4095154284, -2187371499312, 7964242253473, 6052757424558586, -25343867475914910, -25988018018090461664, 123032891453320498449, 163684285184147641156098, -864557405968781387651984, -1448111703094244548802632160

Offset: 0

Ilya Gutkovskiy, Oct 08 2018

sign

For n > 2, a(n) is the n-th term of the logarithmic transform of n-gonal numbers.

N. J. A. Sloane, Transforms
Index to sequences related to polygonal numbers

Cf. A009306, A033464, A300455, A318118, A318124, A320254.

Table[n! SeriesCoefficient[Log[1 + Exp[x] (x + (n/2 - 1) x^2)], {x, 0, n}], {n, 0, 20}]

cp's OEIS Frontend

A318125 a(n) = [x^n] exp(Sum_{k>=1} (-1)^(k+1)x^k(1 + (n - 3)x^k)/(k(1 - x^k)^4)).

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Formula

A320254 a(n) = n! * [x^n] exp(exp(x)(x + (n/2 - 1)x^2)).

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Mathematica

A320255 a(n) = n! * [x^n] log(1 + exp(x)(x + (n/2 - 1)x^2)).

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cp's OEIS Frontend

A318125 a(n) = [x^n] exp(Sum_{k>=1} (-1)^(k+1)*x^k*(1 + (n - 3)*x^k)/(k*(1 - x^k)^4)).

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Programs

Mathematica

Formula

A320254 a(n) = n! * [x^n] exp(exp(x)*(x + (n/2 - 1)*x^2)).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A320255 a(n) = n! * [x^n] log(1 + exp(x)*(x + (n/2 - 1)*x^2)).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A318125 a(n) = [x^n] exp(Sum_{k>=1} (-1)^(k+1)x^k(1 + (n - 3)x^k)/(k(1 - x^k)^4)).

A320254 a(n) = n! * [x^n] exp(exp(x)(x + (n/2 - 1)x^2)).

A320255 a(n) = n! * [x^n] log(1 + exp(x)(x + (n/2 - 1)x^2)).