A035174 -id:A035174 - cp's OEIS frontend

A064556 Ramanujan's tau function (or tau numbers (A000594)) for 10^n.

Original entry on oeis.org

1, -115920, 37534859200, -30328412970240000, -482606811957501440000, -2983637890141033828147200000

Offset: 0

Robert G. Wilson v, Jan 04 2003

sign

Seiichi Manyama, Table of n, a(n) for n = 0..181
Index entries for linear recurrences with constant coefficients, signature (-115920, 124097412800, -11592000000000000, -10000000000000000000000).

Cf. A000594, A035174.

Mathematica
```
Table[ RamanujanTau[10^n], {n, 0, 5}]
```

taup(p, e)={
    if(e==1,
        (65*sigma(p, 11)+691*sigma(p, 5)-691*252*sum(k=1, p-1, sigma(k, 5)*sigma(p-k, 5)))/756
    ,
        my(t=taup(p, 1));
        sum(j=0, e\2,
            (-1)^j*binomial(e-j, e-2*j)*p^(11*j)*t^(e-2*j)
        )
    )
};
a(n)=taup(5,n)*taup(2,n) \\ Charles R Greathouse IV, Sep 06 2015

use bigint; use ntheory ":all"; say "$ ",ramanujan_tau(10 ** $) for 0..19; # Dana Jacobsen, Sep 05 2015

A299206 Ramanujan's tau function (or tau numbers (A000594)) for 5^n.

Original entry on oeis.org

1, 4830, -25499225, -359001100500, -488895969711875, 15167983076643206250, 97133231781274332671875, -271470664160664028370625000, -6054036890966043032024015234375, -15985594659896064584391569753906250, 218396847859403327980436336954599609375

Offset: 0

Seiichi Manyama, Feb 05 2018

sign

Eric Weisstein's World of Mathematics, Tau Function
Index entries for linear recurrences with constant coefficients, signature (4830, -48828125).

Cf. A000594, A000351, A035174, A064556.

RamanujanTau[5^Range[0,10]] (* Harvey P. Dale, Jun 06 2024 *)

PARI
```
{a(n) = ramanujantau(5^n)}
```

G.f.: 1/(1-4830*x+48828125*x^2).

a(n) = A000594(A000351(n)). - Michel Marcus, Feb 05 2018

cp's OEIS Frontend

A064556 Ramanujan's tau function (or tau numbers (A000594)) for 10^n.

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