login
A198403
a(n) = 6^n * n^6.
2
0, 6, 2304, 157464, 5308416, 121500000, 2176782336, 32934190464, 440301256704, 5355700839936, 60466176000000, 642717115324416, 6499837226778624, 63041475422674944, 590045794670739456, 5355700839936000000
OFFSET
0,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (42,-756,7560,-45360,163296,-326592,279936).
FORMULA
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
MATHEMATICA
With[{m=6}, Table[n^m*m^n, {n, 0, 30}]] (* G. C. Greubel, May 18 2022 *)
PROG
(Magma) [6^n*n^6: n in [0..20]]
(PARI) a(n)=6^n*n^6 \\ Charles R Greathouse IV, Jul 06 2017
(SageMath) m=6; [n^m*m^n for n in (0..30)] # G. C. Greubel, May 18 2022
CROSSREFS
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).
Sequence in context: A059203 A254005 A279654 * A369970 A279533 A069643
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Oct 27 2011
STATUS
approved