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A277912 Expansion of ((Product_{n>=1} (1 - x^(11*n))/(1 - x^n)^11) - 1)/11 in powers of x. 6
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 20 01:36 EDT 2019. Contains 324223 sequences. (Running on oeis4.)