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

1, 7, 50, 366, 2760, 21576, 176112, 1512720, 13781376, 134110080, 1401566976, 15780033792, 191537187840, 2503044135936, 35120982067200, 527284915992576, 8439379765788672, 143486382677852160, 2582856448158007296

Offset: 0

Author

Philippe Deléham, Jul 13 2005

Keywords

• easy
• nonn

Comments

Binomial transform of A080954.

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

Links

• Amiram Eldar, Table of n, a(n) for n = 0..448

Crossrefs

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

Programs

Maple

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

Mathematica

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

Formula

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

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

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

Extensions

More terms from Emeric Deutsch, Jul 18 2005