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A053691 11-core partitions of n. 2
1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 45, 66, 79, 102, 121, 154, 176, 220, 248, 297, 330, 430, 452, 552, 605, 720, 777, 935, 990, 1182, 1265, 1485, 1530, 1838, 1892, 2214, 2310, 2684, 2750, 3238, 3289, 3850, 3960, 4500, 4599, 5370, 5404, 6220, 6325, 7238 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..1000 from T. D. Noe)

F. Garvan, D. Kim and D. Stanton, Cranks and t-cores, Inventiones Math. 101 (1990) 1-17.

M. Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

Expansion of f(-x^11)^11 / f(-x) in powers of x where f() is a Ramanujan theta function.

Expansion of q^-5 * etq(q^11)^11 / eta(q) in powers of q. - Michael Somos, Nov 06 2014

Euler transform of period 11 sequence [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -10, ...]. - Michael Somos, Nov 06 2014

G.f. Product_{k>0} (1 - x^(11*k))^11 / (1 - x^k).

EXAMPLE

G.f. = 1 + x + 2*x^2 + 3*x^3 + 5*x^4 + 7*x^5 + 11*x^6 + 15*x^7 + 22*x^8 + ...

G.f. = q^5 + q^6 + 2*q^7 + 3*q^8 + 5*q^9 + 7*q^10 + 11*q^11 + 15*q^12 + ...

MATHEMATICA

m = 50; CoefficientList[ Series[ Product[(1-q^(11*k))^11/(1-q^k), {k, 1, m}], {q, 0, m}], q] (* Jean-Fran├žois Alcover, Jul 26 2011, after g.f. *)

a[ n_] := SeriesCoefficient[ QPochhammer[ x^11]^11 / QPochhammer[ x], {x, 0, n}]; (* Michael Somos, Nov 06 2014 *)

PROG

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^11 + A)^11 / eta(x + A), n))}; /* Michael Somos, Nov 06 2014 */

CROSSREFS

Column t=11 of A175595.

Sequence in context: A261776 A027344 A184645 * A242696 A218510 A026816

Adjacent sequences:  A053688 A053689 A053690 * A053692 A053693 A053694

KEYWORD

easy,nice,nonn,changed

AUTHOR

James A. Sellers, Feb 14 2000

STATUS

approved

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Last modified November 21 22:40 EST 2019. Contains 329383 sequences. (Running on oeis4.)