A198478 -id:A198478 - cp's OEIS frontend

A198402 a(n) = 5^n * n^5.

0, 5, 800, 30375, 640000, 9765625, 121500000, 1313046875, 12800000000, 115330078125, 976562500000, 7863818359375, 60750000000000, 453238525390625, 3282617187500000, 23174285888671875, 160000000000000000, 1083264923095703125

Offset: 0

Vincenzo Librandi, Oct 27 2011

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (30,-375,2500,-9375,18750,-15625).

Cf. A000351, A000584, A097206.

Sequences of the form n^m*m^n: A001477 (m=1), A007758 (m=2), A062074 (m=3), A062075 (m=4), this sequence (m=5), A198403 (m=6), A098803 (m=7), A198404 (m=8), A198478 (m=9), A198479 (m=10), A098880 (m=11).

Magma
```
[5^n*n^5: n in [0..20]]
```

With[{m = 5}, Table[n^m*m^n, {n, 0, 30}]] (* G. C. Greubel, May 18 2022 *)

a(n)=5^n*n^5 \\ Charles R Greathouse IV, Jul 06 2017

m=5; [n^m*m^n for n in (0..30)] # G. C. Greubel, May 18 2022

G.f.: 5*x*(1 + 130*x + 1650*x^2 + 3250*x^3 + 625*x^4)/(1-5*x)^6. - Colin Barker, Apr 30 2013
E.g.f.: 5*x*(1 + 75*x + 625*x^2 + 1250*x^3 + 625*x^4)*exp(5*x). - G. C. Greubel, May 18 2022
a(n) = A000351(n)*A000584(n). - Michel Marcus, May 19 2022

A198403 a(n) = 6^n * n^6.

Original entry on oeis.org

0, 6, 2304, 157464, 5308416, 121500000, 2176782336, 32934190464, 440301256704, 5355700839936, 60466176000000, 642717115324416, 6499837226778624, 63041475422674944, 590045794670739456, 5355700839936000000

Offset: 0

Vincenzo Librandi, Oct 27 2011

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (42,-756,7560,-45360,163296,-326592,279936).

Cf. A000400, A001014.

Sequences of the form n^m*m^n: A001477 (m=1), A007758 (m=2), A062074 (m=3), A062075 (m=4), A198402 (m=5), this sequence (m=6), A098803 (m=7), A198404 (m=8), A198478 (m=9), A198479 (m=10), A098880 (m=11).

Magma
```
[6^n*n^6: n in [0..20]]
```

With[{m=6}, Table[n^m*m^n, {n,0,30}]] (* G. C. Greubel, May 18 2022 *)

a(n)=6^n*n^6 \\ Charles R Greathouse IV, Jul 06 2017

m=6; [n^m*m^n for n in (0..30)] # G. C. Greubel, May 18 2022

G.f.: 6*x*(1 + 336*x + 8856*x^2 + 12096*x^3 + 1296*x^4)/(1-6*x)^7. - Colin Barker, Apr 30 2013
E.g.f.: 6*x*(1 + 186*x + 3240*x^2 + 14040*x^3 + 19440*x^4 + 7776*x^5)*exp(6*x). - G. C. Greubel, May 18 2022
a(n) = A000400(n)*A001014(n). - Michel Marcus, May 19 2022
a(n) = 42*a(n-1) - 756*a(n-2) + 7560*a(n-3) - 45360*a(n-4) + 163296*a(n-5) - 326592*a(n-6) + 279936*a(n-7). - Wesley Ivan Hurt, Sep 04 2022

cp's OEIS Frontend

A198402 a(n) = 5^n * n^5.

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