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a(n) = Sum_{k=0..5} (n+k)! * C(5,k).
(Formerly M5361 N2328)
5

%I M5361 N2328 #22 Feb 01 2022 01:32:33

%S 88,326,1631,10112,74046,622704,5900520,62118720,718709040,9059339520,

%T 123521086080,1810829260800,28397649772800,474281518233600,

%U 8403557607244800,157429696667443200,3108814043182848000,64537726313668608000,1405033277277966336000

%N a(n) = Sum_{k=0..5} (n+k)! * C(5,k).

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H T. D. Noe, <a href="/A001347/b001347.txt">Table of n, a(n) for n = -1..100</a>

%H E. Biondi, L. Divieti, G. Guardabassi, <a href="http://dx.doi.org/10.4153/CJM-1970-003-9">Counting paths, circuits, chains and cycles in graphs: A unified approach</a>, Canad. J. Math. 22 1970 22-35.

%t Join[{88}, Table[Sum[(n + k)! Binomial[5, k], {k, 0, 5}], {n, 0, 20}]] (* _T. D. Noe_, Jun 28 2012 *)

%K nonn

%O -1,1

%A _N. J. A. Sloane_