A258793 -id:A258793 - cp's OEIS frontend

A258794 a(n) = [x^n] Product_{k=1..n} 1/(x^(2k)(1-x^k)^3).

1, 10, 294, 10592, 433350, 19269768, 910578172, 45070219993, 2313935076132, 122371149279812, 6631958513821919, 366896706349540194, 20656935779581469141, 1180759136663178459661, 68388869189063880001236, 4007252716834400744174729, 237231272998203169561835387

Offset: 0

Vaclav Kotesovec, Jun 10 2015

nonn

Cf. A258788, A258789, A258790, A258791, A258792, A258793, A258795, A258796.

Table[SeriesCoefficient[1/Product[x^(2*k)*(1-x^k)^3, {k, 1, n}], {x, 0, n}], {n, 0, 20}]
Table[SeriesCoefficient[1/Product[1-x^k, {k, 1, n}]^3, {x, 0, n*(n+2)}], {n, 0, 20}]

a(n) ~ c * d^n / n^3, where d = 70.2047644028747363037741119300640924984352825702388550206966992563459... = r^5/(r-1)^3, where r is the root of the equation polylog(2, 1-r) + (5*log(r)^2)/6 = 0, c = 4.0416205700754156... .

A258789 a(n) = [x^n] Product_{k=1..n} 1/(x^(2k)(1-x^k)).

Original entry on oeis.org

1, 1, 5, 27, 169, 1115, 7760, 55748, 411498, 3101490, 23785645, 185064559, 1457664666, 11602828475, 93205739436, 754751603157, 6155229065861, 50515624923790, 416930705579538, 3458726257239312, 28825340825747729, 241245120218823892, 2026803168946440648

Offset: 0

Vaclav Kotesovec, Jun 10 2015

nonn

Vaclav Kotesovec, Table of n, a(n) for n = 0..380

Cf. A258268, A258788, A258791, A258793, A258794.

T:=proc(n, k) option remember; `if`(n=0 or k=1, 1, T(n, k-1) + `if`(n

Table[SeriesCoefficient[1/Product[x^(2*k)*(1-x^k), {k, 1, n}], {x, 0, n}], {n, 0, 30}]
Table[SeriesCoefficient[1/Product[1-x^k, {k, 1, n}], {x, 0, n*(n+2)}], {n, 0, 30}]

a(n) ~ c * d^n / n^2, where d = A258268 = 9.15337019245412246194853029240135454007332720412184884968926320147613... = r^3/(r-1), where r is the root of the equation polylog(2, 1-r) + 3*log(r)^2/2 = 0, c = 0.8069142856822510276258439534144172057548... .

A258791 a(n) = [x^n] Product_{k=1..n} 1/(x^k*(1-x^k)^2).

Original entry on oeis.org

1, 3, 20, 158, 1307, 11352, 102538, 954904, 9112038, 88723163, 878714118, 8829998320, 89848944237, 924291213496, 9600148608620, 100565064076006, 1061498376477423, 11281275452880277, 120635822090127386, 1297256892395670322, 14021436433125959714

Offset: 0

Vaclav Kotesovec, Jun 10 2015

nonn

Cf. A258788, A258789, A258793, A258794.

Table[SeriesCoefficient[1/Product[x^k*(1-x^k)^2, {k, 1, n}], {x, 0, n}], {n, 0, 25}]
Table[SeriesCoefficient[1/Product[1-x^k, {k, 1, n}]^2, {x, 0, n*(n+3)/2}], {n, 0, 25}]

a(n) ~ c * d^n / n^(5/2), where d = 12.0708016857156441729965623654557363850943928675996965027830903372727... = r^3/(r-1)^2, where r is the root of the equation polylog(2, 1-r) + (3*log(r)^2)/4 = 0, c = 8.36819319541... .

A258795 a(n) = [x^n] Product_{k=1..n} 1/(x^(3k)(1-x^k)^2).

Original entry on oeis.org

1, 5, 112, 3216, 104112, 3661517, 136580866, 5323418568, 214685704402, 8897404908604, 377068336570902, 16280261371485594, 714081427614467553, 31747177836376617322, 1428084942303149795972, 64902413675181889657064, 2976483322906106920966911

Offset: 0

Vaclav Kotesovec, Jun 10 2015

nonn

Cf. A258788, A258790, A258791, A258792, A258793, A258794, A258796.

Table[SeriesCoefficient[1/Product[x^(3*k)*(1-x^k)^2, {k, 1, n}], {x, 0, n}], {n, 0, 20}]
Table[SeriesCoefficient[1/Product[1-x^k, {k, 1, n}]^2, {x, 0, n*(3*n+5)/2}], {n, 0, 20}]

a(n) ~ c * d^n / n^(5/2), where d = 53.0676066669703028123492951828168330443393201750491213178019371417684... = r^5/(r-1)^2, where r is the root of the equation polylog(2, 1-r) + (5*log(r)^2)/4 = 0, c = 0.983501005499107... .

cp's OEIS Frontend

A258794 a(n) = [x^n] Product_{k=1..n} 1/(x^(2k)(1-x^k)^3).

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A258789 a(n) = [x^n] Product_{k=1..n} 1/(x^(2k)(1-x^k)).

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Mathematica

Formula

A258791 a(n) = [x^n] Product_{k=1..n} 1/(x^k*(1-x^k)^2).

Views

Author

Keywords

Crossrefs

Programs

Mathematica

Formula

A258795 a(n) = [x^n] Product_{k=1..n} 1/(x^(3k)(1-x^k)^2).

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Formula

cp's OEIS Frontend

A258794 a(n) = [x^n] Product_{k=1..n} 1/(x^(2*k)*(1-x^k)^3).

Views

Author

Keywords

Crossrefs

Programs

Mathematica

Formula

A258789 a(n) = [x^n] Product_{k=1..n} 1/(x^(2*k)*(1-x^k)).

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Mathematica

Formula

A258791 a(n) = [x^n] Product_{k=1..n} 1/(x^k*(1-x^k)^2).

Views

Author

Keywords

Crossrefs

Programs

Mathematica

Formula

A258795 a(n) = [x^n] Product_{k=1..n} 1/(x^(3*k)*(1-x^k)^2).

Views

Author

Keywords

Crossrefs

Programs

Mathematica

Formula

A258794 a(n) = [x^n] Product_{k=1..n} 1/(x^(2k)(1-x^k)^3).

A258789 a(n) = [x^n] Product_{k=1..n} 1/(x^(2k)(1-x^k)).

A258795 a(n) = [x^n] Product_{k=1..n} 1/(x^(3k)(1-x^k)^2).