%I M4352 N1822 #29 Feb 01 2022 01:32:05
%S 7,16,49,212,1158,7584,57720,499680,4843440,51932160,610001280,
%T 7787404800,107336275200,1588369305600,25113574886400,422465999155200,
%U 7533512034048000,141940206600192000,2817400117948416000,58760985871171584000,1284693905417674752000
%N a(n) = Sum_{k = 0..3} (n+k)! C(3,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="/A001345/b001345.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[{7}, Table[Sum[(n + k)! Binomial[3, k], {k, 0, 3}], {n, 0, 20}]] (* _T. D. Noe_, Jun 28 2012 *)
%o (PARI) a(n) = if (n == -1, 7, sum(k=0, 3, (n+k)!*binomial(3, k))); \\ _Michel Marcus_, Jun 30 2017
%Y Cf. A001346, A001347.
%K easy,nonn
%O -1,1
%A _N. J. A. Sloane_
%E More terms from _Sean A. Irvine_, Jun 19 2012