%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