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A053693 Number of self-conjugate 8-core partitions of n. 1
1, 1, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 1, 1, 5, 2, 3, 4, 4, 5, 3, 4, 4, 6, 4, 5, 6, 4, 5, 7, 6, 7, 7, 5, 7, 7, 6, 5, 8, 5, 5, 6, 6, 6, 13, 11, 4, 11, 7, 9, 9, 6, 11, 12, 10, 8, 13, 9, 8, 15, 9, 7, 12, 8, 10, 14, 9, 10, 13, 13, 8, 16, 12, 12, 15, 8, 9, 14, 12, 11, 19, 11, 12, 18, 14, 11, 17 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,9

LINKS

Table of n, a(n) for n=0..90.

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

FORMULA

Euler transform of period 16 sequence [ 1, -1, 1, 0, 1, -1, 1, 0, 1, -1, 1, 0, 1, -1, 1, -4, ...]. - Michael Somos, Apr 28 2003

Expansion of q^(-21/8) * eta(q^2)^2 * eta(q^16)^4 / (eta(q) * eta(q^4)) in powers of q. - Michael Somos, Apr 28 2003

G.f.: product((1-q^(16*i))^4*(1-q^(4*i-2))/(1-q^(2*i-1)), i=1..infinity)

EXAMPLE

G.f. = 1 + x + x^3 + x^4 + x^5 + x^6 + x^7 + 2*x^8 + 2*x^9 + 2^x*10 + 2*x^11 + ...

G.f. = q^21 + q^29 + q^45 + q^53 + q^61 + q^69 + q^77 + 2*q^85 + 2*q^93 + 2*q^101 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ QPochhammer[ x^2]^2 QPochhammer[ x^16]^4 / (QPochhammer[ x] QPochhammer[ x^4]), {x, 0, n}]; (* Michael Somos, Feb 22 2015 *)

PROG

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^2 * eta(x^16 + A)^4 / (eta(x + A) * eta(x^4 + A)), n))}; /* Michael Somos, Apr 28 2003 */

CROSSREFS

Cf. A053692.

Sequence in context: A132011 A054893 A090617 * A330324 A291309 A280472

Adjacent sequences:  A053690 A053691 A053692 * A053694 A053695 A053696

KEYWORD

easy,nonn

AUTHOR

James A. Sellers, Feb 14 2000

STATUS

approved

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Last modified April 7 13:36 EDT 2020. Contains 333305 sequences. (Running on oeis4.)