cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-6 of 6 results.

A089802 Expansion of q^(-1/3) * (theta_4(q^3) - theta_4(q^(1/3))) / 2 in powers of q.

Original entry on oeis.org

1, -1, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
Offset: 0

Views

Author

Eric W. Weisstein, Nov 12 2003

Keywords

Comments

Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
Number 10 of the 14 primitive eta-products which are holomorphic modular forms of weight 1/2 listed by D. Zagier on page 30 of "The 1-2-3 of Modular Forms". - Michael Somos, May 04 2016

Examples

			G.f. = 1 - x - x^5 + x^8 + x^16 - x^21 - x^33 + x^40 + x^56 - x^65 - x^85 + ...
G.f. = q - q^4 - q^16 + q^25 + q^49 - q^64 - q^100 + q^121 + q^169 - q^196 + ...

Links

Crossrefs

Cf. A001082, A002448, A089801, A089812.

Programs

  • Mathematica
    a[ n_] := SeriesCoefficient[ (EllipticTheta[ 4, 0, x^3] - EllipticTheta[ 4, 0, x^(1/3)]) / (2 x^(1/3)), {x, 0, n}]; (* Michael Somos, Jun 30 2015 *)
a[ n_] := SeriesCoefficient[ QPochhammer[ x, x^2] EllipticTheta[ 2, 0, x^(3/2)] / (2 x^(3/8)), {x, 0, n}]; (* Michael Somos, Jun 30 2015 *)
a[ n_] := SeriesCoefficient[ QPochhammer[ x, x^2] QPochhammer[ -x^3, x^3] QPochhammer[ x^6], {x, 0, n}]; (* Michael Somos, Jun 30 2015 *)
a[ n_] := SeriesCoefficient[ QPochhammer[ x, x^6] QPochhammer[ x^5, x^6] QPochhammer[ x^6], {x, 0, n}]; (* Michael Somos, Jun 30 2015 *)
a[ n_] := (-1)^n Sign @ SquaresR[ 1, 3 n + 1]; (* Michael Somos, Jun 30 2015 *)
  • PARI
    {a(n) = (-1)^n * issquare(3*n + 1)}; /* Michael Somos, Apr 12 2005 */

Formula

Expansion of q^(-1/3) * (eta(q) * eta(q^6)^2) / (eta(q^2) * eta(q^3)) in powers of q. - Michael Somos, Apr 12 2005
Expansion of chi(-x) * psi(x^3) in powers of x where psi(), chi() are Ramanujan theta functions. - Michael Somos, Dec 23 2011
Expansion of f(-x, -x^5) in powers of x, where f(, ) is Ramanujan's general theta function.
a(n) = b(3*n + 1) where b() is multiplicative with b(3^e) = 0^e, b(2^e) = - (1 + (-1)^e) / 2 if e>0, b(p^e) = (1 + (-1)^e) / 2 if p>3.
G.f. is a period 1 Fourier series which satisfies f(-1 / (144 t)) = 8^(1/2) (t/i)^(1/2) g(t) where q = exp(2 Pi i t) and g() is the g.f. for A089812. - Michael Somos, Dec 23 2011
Euler transform of period 6 sequence [-1, 0, 0, 0, -1, -1, ...]. - Michael Somos, Apr 12 2005
abs(a(n)) is the characteristic function of A001082. - Michael Somos, Oct 31 2005
G.f.: Sum_{k in Z} (-1)^k * x^((3*k^2 - 2*k)) = Product_{k>0} (1 - x^(6*k)) * (1 - x^(6*k - 1)) * (1 - x^(6*k - 5)). - Michael Somos, Oct 31 2005
A002448(3*n + 1) = -2 * a(n). - Michael Somos, Jul 07 2006
a(n) = (-1)^n * A089801(n).
a(n) = -(1/n)*Sum_{k=1..n} A284362(k)*a(n-k), a(0) = 1. - Seiichi Manyama, Mar 25 2017

Extensions

Corrected by N. J. A. Sloane, Nov 05 2005

A089810 Expansion of Jacobi theta function theta_3(Pi/6, q) in powers of q.

Original entry on oeis.org

1, 1, 0, 0, -1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0
Offset: 0

Views

Author

Eric W. Weisstein, Nov 12 2003

Keywords

Comments

Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
This is an example of the quintuple product identity in the form f(a*b^4, a^2/b) - (a/b) * f(a^4*b, b^2/a) = f(-a*b, -a^2*b^2) * f(-a/b, -b^2) / f(a, b) where a = -x^5, b = -x. - Michael Somos, Jul 12 2012
Convolution square is A258279. - Michael Somos, May 25 2015
Number 8 of the 14 primitive eta-products which are holomorphic modular forms of weight 1/2 listed by D. Zagier on page 30 of "The 1-2-3 of Modular Forms". - Michael Somos, May 04 2016

Examples

			G.f. = 1 + q - q^4 - 2*q^9 - q^16 + q^25 + 2*q^36 + q^49 - q^64 - 2*q^81 + ...

Links

Crossrefs

Cf. A002448, A080995, A089801, A089802, A089807, A089812, A204843, A204853, A258279.
Cf. A000700, A000122, A010054, A121373.

Programs

  • Mathematica
    a[ n_] := SeriesCoefficient[ EllipticTheta[ 3, Pi/6, q], {q, 0, n}]; (* Michael Somos, Nov 14 2011 *)
a[ n_] := SeriesCoefficient[ (3 EllipticTheta[ 4, 0, q^9] - EllipticTheta[ 4, 0, q])  /2, {q, 0, n}]; (* Michael Somos, Nov 14 2011 *)
QP = QPochhammer; s = QP[q^2]^2*(QP[q^3] / (QP[q]*QP[q^6])) + O[q]^100; CoefficientList[s, q] (* Jean-François Alcover, Nov 09 2015, adapted from PARI *)
  • PARI
    {a(n) = my(x); if( n<1, n==0, issquare(n, &x) * (1 + (n%3==0)) * (-1)^((1 + x) \ 3))}; /* Michael Somos, Nov 05 2005 */
  • PARI
    {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^2 * eta(x^3 + A) / (eta(x + A) * eta(x^6 + A)), n))}; /* Michael Somos, Jan 26 2008 */

Formula

Expansion of Jacobi theta function (3theta_4(q^9) - theta_4(q)) / 2 in powers of q.
a(n) is multiplicative with a(0)=1, a(2^e) = -(1 + (-1)^e)/2, if e>0, a(3^e) = -2(1 + (-1)^e)/2 if e>0, a(p^e) = (1 + (-1)^e)/2 otherwise.
From Michael Somos, Nov 05 2005: (Start)
Euler transform of period 6 sequence [ 1, -1, 0, -1, 1, -1, ...].
G.f.: (Sum_{k in Z} 3 * (-x)^((3*k)^2) - (-x)^(k^2)) / 2 = Product_{k>0} (1 - x^(2*k)) / ((1 - x^(6*k - 1)) * (1 - x^(6*k-5))).
Expansion of eta(q^2)^2 * eta(q^3) / (eta(q) * eta(q^6)) in powers of q. (End)
Expansion of psi(q) * chi(-q^3) in powers of q where psi(), chi() are Ramanujan theta functions. - Michael Somos, Sep 16 2007
Expansion of (3 * phi(-q^9) - phi(-q)) / 2 in powers of q where phi() is a Ramanujan theta function.
From Michael Somos, Sep 17 2007: (Start)
Expansion of Jacobi theta function theta_3(Pi/6, q) in powers of q.
Expansion of f(x*w, x/w) in powers of x where w is a primitive sixth root of unity and f() is Ramanujan's two-variable theta function. (End)
From Michael Somos, Jan 26 2008: (Start)
G.f. is a period 1 Fourier series which satisfies f(-1 / (144 t)) = 72^(1/2) (t/i)^(1/2) g(t) where q = exp(2 Pi i t) and g(t) is the g.f. for A080995.
G.f.: Product_{k>0} (1 - x^(2*k)) / (1 - x^k + x^(2*k)). (End)
a(3*n + 2) = a(4*n + 2) = a(4*n + 3) = a(5*n + 2) = a(5*n + 3) = a(8*n + 5) = a(9*n + 3) = a(9*n + 6) = 0. a(3*n + 1) = A089802(n). a(4*n) = A089807(n). a(9*n) = A002448(n).
a(n) = (floor(sqrt(n))-floor(sqrt(n-1)))*(abs(2-4*sin((floor(sqrt(n))+1)*Pi/3)^2) - 4*sin((floor(sqrt(n))+2)*Pi/3)^2)*(-1)^floor(floor(sqrt(n)-1)/3). - Mikael Aaltonen, Jan 17 2015
From Michael Somos, May 25 2015: (Start)
a(n) = (-1)^n * A089807(n) = A204843(4*n) = A204853(4*n).
a(8*n + 1) = A089812(n). a(12*n + 4) = - A089801(n). (End)
Sum_{k=1..n} abs(a(k)) ~ (4/3)*sqrt(n). - Amiram Eldar, Jan 27 2024

A089807 Expansion of Jacobi theta function (3theta_3(q^9)-theta_3(q))/2.

Original entry on oeis.org

1, -1, 0, 0, -1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1
Offset: 0

Views

Author

Eric W. Weisstein, Nov 12 2003

Keywords

Comments

Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
This is an example of the quintuple product identity in the form f(a*b^4, a^2/b) - (a/b) * f(a^4*b, b^2/a) = f(-a*b, -a^2*b^2) * f(-a/b, -b^2) / f(a, b) where a = x^5, b = x. - Michael Somos, Jul 12 2012
Number 11 of the 14 primitive eta-products which are holomorphic modular forms of weight 1/2 listed by D. Zagier on page 30 of "The 1-2-3 of Modular Forms". - Michael Somos, May 04 2016

Examples

			G.f. = 1 - q - q^4 + 2*q^9 - q^16 - q^25 + 2*q^36 - q^49 - q^64 + 2*q^81 + ...

Links

Crossrefs

Related to the 14 primitive eta-products which are holomorphic modular forms of weight 1/2: A000122, A002448, A010054, A010815, A080995, A089801, A089802, this sequence, A089810, A089812, A106459, A121373, A133985, A133988. - Seiichi Manyama, May 15 2017
Cf. A000700, A000122, A010054, A121373.

Programs

  • Mathematica
    a[ n_] := SeriesCoefficient[ EllipticTheta[ 3, Pi/3, q], {q, 0, n}]; (* Michael Somos, Jul 12 2012 *)
a[ n_] := SeriesCoefficient[ (3 EllipticTheta[ 3, 0, q^9] - EllipticTheta[ 3, 0, q])/2, {q, 0, n}]; (* Michael Somos, Jul 12 2012 *)
a[ n_] := SeriesCoefficient[ QPochhammer[ -q^3, q^6] EllipticTheta[ 2, 0, Sqrt[ -q]] / (2 (-q)^(1/8)), {q, 0, n}] (* Michael Somos, Jul 12 2012 *);
  • PARI
    {a(n) = if( n<1, n==0, issquare(n) * (3*(n%3==0) - 1))}; /* Michael Somos, Nov 05 2005 */

Formula

a(n) = -b(n) where b() is multiplicative with b(3^e) = -2(1 + (-1)^e) / 2 if e>0, b(p^e) = (1 + (-1)^e) / 2 otherwise.
From Michael Somos, Nov 05 2005: (Start)
Expansion of eta(q) * eta(q^4) * eta(q^6)^2 / (eta(q^2) * eta(q^3) * eta(q^12)) in powers of q.
Euler transform of period 12 sequence [ -1, 0, 0, -1, -1, -1, -1, -1, 0, 0, -1, -1, ...].
G.f.: (Sum_{k in Z} 3 * x^((3*k)^2) - x^(k^2)) / 2 = Product_{k>0} (1 - x^k) / ((1 - x^(12*k - 2)) * (1 - x^(12*k - 3)) * (1 - x^(12*k - 9)) * (1 - x^(12*k - 10))). (End)
Expansion of Jacobi theta function theta_3(Pi/3, q) in powers of q. - Michael Somos, Jan 26 2006
Expansion of chi(q^3) * psi(-q) in powers of q where chi(), psi() are Ramanujan theta functions. - Michael Somos, May 19 2007
Expansion of f(x*w, x/w) in powers of x where w is a primitive cube root of unity and f(, ) is Ramanujan's general theta function. - Michael Somos, Sep 17 2007
G.f. is a period 1 Fourier series which satisfies f(-1 / (36 t)) = 18^(1/2) (t/i)^(1/2) g(t) where q = exp(2 Pi i t) and g() is the g.f. for A089801.
a(n) = (-1)^n * A089810(n). - Michael Somos, Jan 20 2012
For n > 0, a(n) = (floor(sqrt(n))-floor(sqrt(n-1)))*(2-4*sin(floor(sqrt(n))*Pi/3)^2). - Mikael Aaltonen, Jan 17 2015
Sum_{k=1..n} abs(a(k)) ~ (4/3)*sqrt(n). - Amiram Eldar, Jan 27 2024

A133988 Expansion of phi(x) / chi(x^3) in powers of x where phi(), chi() are Ramanujan theta functions.

Original entry on oeis.org

1, 2, 0, -1, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0
Offset: 0

Views

Author

Michael Somos, Oct 01 2007

Keywords

Comments

Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
This is an example of the quintuple product identity in the form f(a*b^4, a^2/b) - (a/b) * f(a^4*b, b^2/a) = f(-a*b, -a^2*b^2) * f(-a/b, -b^2) / f(a, b) where a = x^2, b = -x. - Michael Somos, Jan 21 2012
Number 13 of the 14 primitive eta-products which are holomorphic modular forms of weight 1/2 listed by D. Zagier on page 30 of "The 1-2-3 of Modular Forms". - Michael Somos, May 04 2016

Examples

			G.f. = 1 + 2*x - x^3 + x^6 - 2*x^10 - x^15 - x^21 - 2*x^28 + x^36 - x^45 + ...
G.f. = q + 2*q^9 - q^25 + q^49 - 2*q^81 - q^121 - q^169 - 2*q^225 + q^289 - ...

Links

Crossrefs

Cf. A089812, A133985.

Programs

  • Mathematica
    a[ n_] := (-1)^Quotient[n, 3] Mod[n + 1, 3] Boole[ IntegerQ[ Sqrt[8 n + 1]]]; (* Michael Somos, Oct 30 2015 *)
a[ n_] := SeriesCoefficient[ EllipticTheta[ 3, 0, x]  QPochhammer[ x^3, -x^3], {x, 0, n}]; (* Michael Somos, Oct 30 2015 *)
  • PARI
    {a(n) = (-1)^(n\3) * ((n + 1)%3) * issquare( 8*n + 1)};
  • PARI
    {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^5 * eta(x^3 + A) * eta(x^12 + A) / (eta(x + A) * eta(x^4 + A) * eta(x^6 + A))^2, n))};

Formula

Expansion of q^(-1/8) * eta(q^2)^5 * eta(q^3) * eta(q^12) / ( eta(q) * eta(q^4) * eta(q^6) )^2 in powers of q.
Expansion of psi(-x) + 3 * x * psi(-x^9) in powers of x where psi() is a Ramanujan theta function.
Expansion of f(x, x^5) * f(x) / f(-x^6) = f(-x^3, x^6) + x * f(1, -x^9) in powers of x where f(, ) is Ramanujan's general theta function.
Expansion of phi(x^9) / chi(x^3) + 2 * x * psi(-x^9) in powers of x where phi(), chi() are Ramanujan theta functions.
Euler transform of period 12 sequence [ 2, -3, 1, -1, 2, -2, 2, -1, 1, -3, 2, -1, ...].
a(n) = b(8*n + 1) where b() is multiplicative with b(3^(2*e)) = -2 * (-1)^e, b(p^(2*e)) = (-1)^e if p == 3, 5 (mod 8), b(p^(2*e)) = +1 if p == 1, 7 (mod 8) and b(p^(2*e-1)) = b(2^e) = 0 if e>0.
G.f. is a period 1 Fourier series which satisfies f(-1 / (2304 t)) = 12 (t/i)^(1/2) g(t) where q = exp(2 Pi i t) and g() is the g.f. for A133985.
G.f.: Sum_{k>0} (-1)^floor(k/2) * (x^((k^2 - k)/2) + 3 * x^(9*(k^2 - k)/2 + 1) ).
G.f.: Sum_{k in Z} (-1)^(k + floor(k/2)) * x^(3*k * (3*k + 1) / 2) * ( x^(-3*k) + x^(3*k + 1) ).
a(n) = (-1)^n * A089812(n).
a(3*n) = A133985(n). a(3*n + 2) = 0. - Michael Somos, Oct 30 2015

A101230 Number of partitions of 2n in which both odd parts and parts that are multiples of 3 occur with even multiplicities. There is no restriction on the other even parts.

Original entry on oeis.org

1, 2, 4, 7, 12, 20, 32, 50, 76, 113, 166, 240, 343, 484, 676, 935, 1282, 1744, 2355, 3158, 4208, 5573, 7340, 9616, 12536, 16266, 21012, 27028, 34628, 44196, 56204, 71226, 89964, 113270, 142180, 177948, 222089, 276430, 343172, 424959, 524966
Offset: 0

Views

Author

Noureddine Chair, Dec 16 2004

Keywords

Comments

Note that if a partition of n has odd parts occur with even multiplicities then n must be even. This is the reason for only looking at partitions of 2n. - Michael Somos, Mar 04 2012

Examples

			a(8)=12 because 8 = 4+4 = 4+2+2 = 4+2+1+1 = 4+1+1+1+1 = 3+3+2 = 3+3+1+1 = 2+2+2+2 = 2+2+2+1+1 = 2+2+1+1+1+1 = 2+1+1+1+1+1+1 = 1+1+1+1+1+1+1+1.
1 + 2*x + 4*x^2 + 7*x^3 + 12*x^4 + 20*x^5 + 32*x^6 + 50*x^7 + 76*x^8 + 113*x^9 + ...
1/q + 2*q^7 + 4*q^15 + 7*q^23 + 12*q^31 + 20*q^39 + 32*q^47 + 50*q^55 + 76*q^63 + ...

Links

Crossrefs

Cf. A000041, A003105, A015128, A089812, A098151.

Programs

  • Maple
    series(product((1+x^k)/((1-x^k)*(1+x^(3*k))),k=1..100),x=0,100);
  • Mathematica
    nmax = 50; CoefficientList[Series[Product[(1+x^(3*k-1))*(1+x^(3*k-2)) / (1-x^k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 01 2015 *)
  • PARI
    {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A) * eta(x^3 + A) / (eta(x + A)^2 * eta(x^6 + A)), n))} /* Michael Somos, Mar 04 2012 */

Formula

G.f.: product_{k>0}(1+x^k)/((1-x^k)(1+x^(3k)))= Theta_4(0, x^3)/theta(0, x)1/product_{k>0}(1-x^(3k)).
Euler transform of period 6 sequence [2, 1, 1, 1, 2, 1, ...]. - Vladeta Jovovic, Dec 17 2004
Expansion of q^(1/8) * eta(q^2) * eta(q^3) / (eta(q)^2 * eta(q^6)) in powers of q. - Michael Somos, Mar 04 2012
Convolution inverse of A089812. - Michael Somos, Mar 04 2012
Convolution product of A000041 and A003105. - Michael Somos, Mar 04 2012
a(n) ~ exp(2*Pi*sqrt(2*n)/3) / (6*n). - Vaclav Kotesovec, Sep 01 2015

A089813 Expansion of Jacobi theta function (theta_2(q) - 3*theta_2(q^9))/(2 q^(1/4)) in powers of q.

Original entry on oeis.org

1, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
Offset: 0

Views

Author

Eric W. Weisstein, Nov 12 2003

Keywords

Comments

This is the sequence A089812 with interleaved zeros. - Michael Somos, Nov 21 2017

Examples

			G.f. = 1 - 2*x^2 + x^6 + x^12 - 2*x^20 + x^30 + x^42 - 2*x^56 + x^72 + x^90 - 2*x^110 + ...
G.f. = q - 2*q^9 + q^25 + q^49 - 2*q^81 + q^121 + q^169 - 2*q^225 + q^289 + q^361 + ...

Links

Crossrefs

Cf. A089812.

Programs

  • Mathematica
    A089813[n_] := SeriesCoefficient[(EllipticTheta[2, 0, q] - 3*EllipticTheta[2, 0, q^9])/(2 q^(1/4), {q, 0, n}]; Table[A089813[n], {n, 0, 50}] (* G. C. Greubel, Nov 20 2017 *)
a[ n_] := SeriesCoefficient[ QPochhammer[ q^2]^2 QPochhammer[ q^12] / (QPochhammer[q ^4] QPochhammer[ q^6]), {q, 0, n}]; (* Michael Somos, Nov 21 2017 *)
  • PARI
    {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^2 * eta(x^12 + A) / (eta(x^4 + A) * eta(x^6 + A)), n))}; /* Michael Somos, Nov 21 2017 */
  • PARI
    lista(nn) = {q='q+O('q^nn); Vec(eta(q^2)^2*eta(q^12)/(eta(q^4)*eta(q^6)))} \\ Altug Alkan, Mar 22 2018

Formula

Euler transform of period 12 sequence [0, -2, 0, -1, 0, -1, 0, -1, 0, -2, 0, -1, ...]. - Michael Somos, Nov 21 2017
Showing 1-6 of 6 results.

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