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.

A124996 a(n) is the constant term in the expansion of Product_{k=1..n} (x^k + 1/x^k)^4.

Original entry on oeis.org

1, 6, 44, 426, 4658, 55260, 689508, 8914872, 118374410, 1604658420, 22115171280, 308940507202, 4364729023812, 62256518307724, 895294865045296, 12966655239260890, 188967013096930258, 2769003814616561636, 40773380119956434784, 603008173331642200144
Offset: 0

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Author

N. J. A. Sloane, Jul 12 2008

Keywords

Crossrefs

For constant term in expansion of Product_{k=1..n} (x^k + 1/x^k)^q for other values of q see A063865, A047653, A124995.

Programs

  • PARI
    a(n) = polcoef(prod(k=1, n, (x^k + 1/x^k)^4), 0); \\ Michel Marcus, Jan 07 2021

Formula

a(n) ~ sqrt(3) * 16^n / (sqrt(2*Pi) * n^(3/2)). - Vaclav Kotesovec, Jan 07 2021

A350282 a(n) is the constant term in the expansion of Product_{k=1..n} (x^k + 1/x^k)^n.

Original entry on oeis.org

1, 0, 4, 62, 4658, 0, 2319512420, 14225426190522, 361926393013029354, 0, 16231015449888734994721650504, 28330316118212024049511095643949434, 200866780133770636272812495083578779133456, 0
Offset: 0

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Author

Seiichi Manyama, Dec 23 2021

Keywords

Comments

a(n) is the coefficient of x^(n^2 * (n+1)/2) in Product_{k=0..n} (1 + x^(2*k))^n.

Crossrefs

Programs

  • PARI
    a(n) = polcoef(prod(k=1, n, x^k+1/x^k)^n, 0);
    
  • PARI
    a(n) = polcoef(prod(k=1, n, 1+x^(2*k))^n, n^2*(n+1)/2);

Formula

a(4*n+1) = 0.

A369372 a(n) is the constant term in expansion of Product_{k=1..n} (x^k + 1 + 1/x^k)^3.

Original entry on oeis.org

1, 7, 85, 1437, 26707, 534513, 11255951, 245612031, 5503639327, 125900330437, 2928092906281, 69026845135479, 1645689594867257, 39611576627651927, 961279033420170871, 23494000801494204647, 577777092945262623161, 14287061769367391787065, 355010279665452190629001
Offset: 0

Views

Author

Ilya Gutkovskiy, Jan 21 2024

Keywords

Crossrefs

Programs

  • Mathematica
    Table[Coefficient[Product[(x^k + 1 + 1/x^k)^3, {k, 1, n}], x, 0], {n, 0, 18}]
  • PARI
    a(n) = polcoef(prod(k=1, n, (x^k + 1 + 1/x^k)^3), 0); \\ Michel Marcus, Jan 22 2024
Showing 1-3 of 3 results.