A277912 Expansion of ((Product_{n>=1} (1 - x^(11*n))/(1 - x^n)^11) - 1)/11 in powers of x.

0, 1, 7, 38, 175, 714, 2653, 9139, 29563, 90650, 265401, 746142, 2023566, 5314008, 13554912, 33673525, 81654104, 193646588, 449903128, 1025532912, 2296519589, 5058078488, 10968488747, 23440057192, 49406752403, 102792264765, 211242738976, 429066735314, 861868377262, 1713014236294, 3370525567099

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

G.f.: ((Product_{n>=1} (1 - x^(11*n))/(1 - x^n)^11) - 1)/11.

a(n) ~ 5^(11/4) * exp(4*Pi*sqrt(5*n/11)) / (sqrt(2)*11^(17/4)*n^(13/4)). - Vaclav Kotesovec, Nov 10 2016

Example

G.f. = x + 7*x^2 + 38*x^3 + 175*x^4 + 714*x^5 + 2653*x^6 + ...

Mathematica

nmax = 50; CoefficientList[Series[(Product[(1 - x^(11*j))/(1 - x^j)^11, {j, 1, nmax}] - 1)/11, {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 10 2016 *)
a[ n_] := SeriesCoefficient[ (QPochhammer[ x^11] / QPochhammer[ x]^11 - 1) / 11, {x, 0, n}]; (* Michael Somos, Nov 13 2016 *)

Prog

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x^11 + A) / eta(x + A)^11 - 1) / 11, n))}; /* Michael Somos, Nov 13 2016 */
(PARI) x='x+O('x^66); concat([0], Vec(eta(x^11)/eta(x)^11-1)/11) \\ Joerg Arndt, Nov 27 2016

Crossrefs

Cf. Expansion of ((Product_{n>=1} (1 - x^(k*n))/(1 - x^n)^k) - 1)/k in powers of x: A014968 (k=2), A277968 (k=3), A277974 (k=5), A160549 (k=7), this sequence (k=11).

Sequence in context: A249354 A249021 A114290 * A000531 A296769 A241524

Adjacent sequences: A277909 A277910 A277911 * A277913 A277914 A277915

Keyword

nonn

Author

Seiichi Manyama, Nov 07 2016

Status

approved