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%I #69 Nov 29 2022 01:33:01
%S 1,1,8,162,6144,375000,33592320,4150656720,676457349120,
%T 140587147048320,36288000000000000,11388728893445164800,
%U 4270826380475341209600,1886009588552176549862400,968725766854884321342259200,572622616354851562500000000000
%N a(n) = n!*n^n.
%C a(n) is the product of first n terms of an arithmetic progression with first term n and common difference n. E.g. a(3) = 3*6*9 = 162. - _Amarnath Murthy_, Sep 20 2003
%H Harry J. Smith, <a href="/A061711/b061711.txt">Table of n, a(n) for n = 0..100</a> (corrected by Michel Marcus, Jan 19 2019)
%F E.g.f.: sinh(n*x)^n. - _Vaclav Kotesovec_, Nov 05 2014
%F a(n) = [x^n] 1/(1 - n*x/(1 - n*x/(1 - 2*n*x/(1 - 2*n*x/(1 - 3*n*x/(1 - 3*n*x/(1 - ...))))))), a continued fraction. - _Ilya Gutkovskiy_, Sep 20 2017
%F Sum_{n>=1} 1/a(n) = A336765. - _Amiram Eldar_, Nov 20 2020
%F a(n) ~ exp(-n)*n^(2*n)*sqrt(2*n*Pi). - _Peter Luschny_, Jan 10 2022
%e a(1) = 1!*1^1 = 1.
%e a(2) = 2!*2^2 = 8.
%e a(3) = 3!*3^3 = 162.
%t Table[If[n == 0, 1, n^n] * n!, {n, 0, 20}] (* _Vaclav Kotesovec_, Mar 08 2018 *)
%o (PARI) a(n) = n!*n^n; \\ _Harry J. Smith_, Jul 26 2009
%o (Python)
%o from math import factorial
%o def A061711(n): return factorial(n)*n**n # _Chai Wah Wu_, Sep 03 2022
%o (Magma) [Factorial(n)*n^n: n in [0..30]]; // _G. C. Greubel_, Nov 29 2022
%Y Cf. A036679, A053042, A055775. - _Vladimir Joseph Stephan Orlovsky_, Jan 15 2009
%Y Main diagonal of A131182.
%Y Cf. A336765.
%K easy,nonn
%O 0,3
%A Lorenzo Fortunato (fortunat(AT)pd.infn.it), Jun 19 2001
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