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 1-3 of 3 results.

A160535 Omit first term from A160534 and divide by 7.

Original entry on oeis.org

0, -1, 2, 1, -7, 3, 5, 6, -8, -17, 15, -10, 21, 21, -19, -24, -33, 36, -22, 45, 63, 1, -92, -82, 85, -97, 105, 82, 28, -58, -120, 120, -210, 122, 180, 3, -231, -138, 225, -168, 255, 210, 5, -282, -294, 219, -284, 276, 341, -43, -310, -288, 441, -346, 410, 366, -29, -360, -668, 435, -504, 465, 600, 46, -603, -504
Offset: 0

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Author

N. J. A. Sloane, Nov 14 2009

Keywords

Comments

These are Watson's coefficients beta_n on page 125.

Links

A279613 Expansion of the g.f. of A160534 in powers of A121593.

Original entry on oeis.org

1, -7, 42, -231, 1155, -4998, 15827, -791, -566244, 6506955, -53524611, 369879930, -2218053747, 11306008875, -43772711220, 55203364377, 1172838094533, -16542312772356, 150992704165079, -1130142960861845, 7290759457923816
Offset: 1

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Author

Lynette O'Brien, Dec 15 2016

Keywords

Comments

(eta(q))^7/eta(7*q) in powers of (eta(7*q)/eta(q))^4.
This sequence is u_n in Theorem 6.5 in O'Brien's thesis.

Examples

			G.f.: 1 - 7*x + 42*x^2 - 231*x^3 + 1155*x^4 - 4998*x^5 + ...

References

  • L. O'Brien, Modular forms and two new integer sequences at level 7, Massey University, 2016.

Links

Crossrefs

Cf. A183204, A229111, A279618, A279619.

Formula

(n+1)^4a_7(n+1)=-(26*n^4+52*n^3+58*n^2+32*n+7)a_7(n)-(267*n^4+268*n^2+18)a_7(n-1)-(1274*n^4-2548*n^3+2842*n^2-1568*n+343)a_7(n-2)-2401(n-1)^4a_7(n-3)
with a_7(0)=1, a_7(-1)=a_7(-2)=a_7(-3)=0.
asymptotic conjecture: a(n) ~ C n^(-4/3) 7^n cos( n( arctan( (3*sqrt 3)/13) +Pi -1.083913253)), where C = 6.502807770...

A280666 Expansion of eta(q)^6/eta(q^6) in powers of q.

Original entry on oeis.org

1, -6, 9, 10, -30, 0, 12, 36, 9, -60, -12, -54, 62, 120, 18, -72, -102, -54, -36, 156, 108, 48, -192, -108, 156, 78, 126, -206, -324, -72, 240, 324, 225, -168, -276, -180, 132, 264, 72, -144, -588, -198, 240, 804, 270, -288, -312, -324, 206, 486, 225, -528
Offset: 0

Views

Author

Seiichi Manyama, Jan 07 2017

Keywords

Links

Crossrefs

Cf. A002448 (k=2), A005928 (k=3), A083703 (k=4), A109064 (k=5), this sequence (k=6), A160534 (k=7).

Programs

  • Maple
    with(numtheory):
a:= proc(n) option remember; `if`(n=0, 1, add(add(d*
      `if`(irem(d, 6)=0, -5, -6), d=divisors(j))*a(n-j), j=1..n)/n)
    end:
seq(a(n), n=0..70);  # Alois P. Heinz, Jan 07 2017
  • Mathematica
    QP = QPochhammer; QP[x]^6/QP[x^6] + O[x]^70 // CoefficientList[#, x]& (* Jean-François Alcover, Mar 25 2017 *)
  • PARI
    q='q+O('q^66); Vec( eta(q)^6/eta(q^6) ) \\ Joerg Arndt, Mar 25 2017

Formula

G.f.: Product_{n>0} (1-x^n)^6/(1-x^(6*n)).
Euler transform of period 6 sequence [ -6, -6, -6, -6, -6, -5, ...].
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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