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A108869 E.g.f. : exp(6x)/(1-x). 2

%I #16 Jun 30 2020 05:35:49

%S 1,7,50,366,2760,21576,176112,1512720,13781376,134110080,1401566976,

%T 15780033792,191537187840,2503044135936,35120982067200,

%U 527284915992576,8439379765788672,143486382677852160,2582856448158007296

%N E.g.f. : exp(6x)/(1-x).

%C Binomial transform of A080954.

%C a(n) is the permanent of the n X n matrix with 7's on the diagonal and 1's elsewhere.

%H Amiram Eldar, <a href="/A108869/b108869.txt">Table of n, a(n) for n = 0..448</a>

%F a(n) = n!*Sum_{ k = 0..n } 6^k/k!.

%F a(n) = Sum_{ k = 0..n } A008290(n, k)*7^k.

%F a(n) Sum_{ k = 0..n } k!*C(n, k)*6^(n-k).

%p a:=n->n!*sum(6^k/k!,k=0..n): seq(a(n),n=0..20); # _Emeric Deutsch_, Jul 18 2005

%p restart:F(x):=exp(6*x)/(1-x): f[0]:=F(x): for n from 1 to 20 do f[n]:=diff(f[n-1],x) od: x:=0: seq(f[n],n=0..18); # _Zerinvary Lajos_, Apr 03 2009

%t a[n_] := n! * Sum[6^k/k!, {k, 0, n}]; Array[a, 19, 0] (* _Amiram Eldar_, Jun 30 2020 *)

%Y Cf. A000142, A000522, A008290, A010842, A053486, A053487, A080954.

%K easy,nonn

%O 0,2

%A _Philippe Deléham_, Jul 13 2005

%E More terms from _Emeric Deutsch_, Jul 18 2005

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)