A258795 -id:A258795 - 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... .

A258790 a(n) = [x^n] Product_{k=1..n} 1/(x^(3k)(1-x^k)).

Original entry on oeis.org

1, 1, 6, 48, 411, 3765, 36308, 363446, 3742085, 39405777, 422669224, 4603472960, 50790334667, 566603884871, 6381702580969, 72481863380510, 829331355150992, 9551576115706329, 110654552651370400, 1288710163262774157, 15080440970246785366, 177237948953055593475

Offset: 0

Vaclav Kotesovec, Jun 10 2015

nonn

Vaclav Kotesovec, Table of n, a(n) for n = 0..338

Cf. A258788, A258790, A258792, A258794, A258795, A258796.

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

Table[SeriesCoefficient[1/Product[x^(3*k)*(1-x^k), {k, 1, n}], {x, 0, n}], {n, 0, 25}]
Table[SeriesCoefficient[1/Product[1-x^k, {k, 1, n}], {x, 0, n*(3*n+5)/2}], {n, 0, 25}]

a(n) ~ c * d^n / n^2, where d = 12.8718984948677835397002665286811919572579479691341210018008114644121... = r^4/(r-1), where r is the root of the equation polylog(2, 1-r) + 2*log(r)^2 = 0, c = 0.44720199058408831652920046766862756... .

A258792 a(n) = [x^n] Product_{k=1..n} 1/(x^k*(1-x^k)^3).

Original entry on oeis.org

1, 6, 69, 915, 12978, 194688, 3051617, 49526487, 826910754, 14135805042, 246508115583, 4372617452085, 78714369892152, 1435357362134796, 26472477913596486, 493178852479545556, 9270953614684288962, 175695092091980786166, 3354069936616380522256

Offset: 0

Vaclav Kotesovec, Jun 10 2015

nonn

Cf. A258788, A258790, A258794, A258795, A258796.

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

a(n) ~ c * d^n / n^3, where d = 22.0610202494679061193859054301626736218023392292898139172609021542610... = r^4/(r-1)^3, where r is the root of the equation polylog(2, 1-r) + (2*log(r)^2)/3 = 0, c = 20.953639522741... .

A258796 a(n) = [x^n] Product_{k=1..n} 1/(x^(3k)(1-x^k)^3).

Original entry on oeis.org

1, 15, 882, 67385, 5938518, 575782833, 59765085601, 6529604684991, 742474127495175, 87176531917206953, 10508492822243329854, 1294860745291809207237, 162553748258042032103013, 20735748733960087597815855, 2682101373558320853655174803

Offset: 0

Vaclav Kotesovec, Jun 10 2015

nonn

Cf. A258788, A258790, A258792, A258794, A258795.

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

a(n) ~ c * d^n / n^3, where d = 157.540286488430979726276374519534734829527107090287337321136938826336... = r^6/(r-1)^3, where r is the root of the equation polylog(2, 1-r) + log(r)^2 = 0, c = 1.797864597437050667... .

cp's OEIS Frontend

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

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A258790 a(n) = [x^n] Product_{k=1..n} 1/(x^(3k)(1-x^k)).

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Mathematica

Formula

A258792 a(n) = [x^n] Product_{k=1..n} 1/(x^k*(1-x^k)^3).

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Author

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Crossrefs

Programs

Mathematica

Formula

A258796 a(n) = [x^n] Product_{k=1..n} 1/(x^(3k)(1-x^k)^3).

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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

A258790 a(n) = [x^n] Product_{k=1..n} 1/(x^(3*k)*(1-x^k)).

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Mathematica

Formula

A258792 a(n) = [x^n] Product_{k=1..n} 1/(x^k*(1-x^k)^3).

Views

Author

Keywords

Crossrefs

Programs

Mathematica

Formula

A258796 a(n) = [x^n] Product_{k=1..n} 1/(x^(3*k)*(1-x^k)^3).

Views

Author

Keywords

Crossrefs

Programs

Mathematica

Formula

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

A258790 a(n) = [x^n] Product_{k=1..n} 1/(x^(3k)(1-x^k)).

A258796 a(n) = [x^n] Product_{k=1..n} 1/(x^(3k)(1-x^k)^3).