A075922 - OEIS

%I #8 Dec 27 2017 01:34:13

%S 1,42,1225,30870,722701,16235562,355888225,7683656190,164302593301,

%T 3491636199282,73902587019625,1560051480424710,32874455072382301,

%U 691950889177526202,14553192008156093425,305928163614832076430

%N Third column of triangle A075502.

%C The e.g.f. given below is Sum_{m=0..2} A075513(3,m)*exp(7*(m+1)*x)/2!.

%F a(n) = A075502(n+3, 3) = (7^n)*S2(n+3, 3) with S2(n, m) := A008277(n, m) (Stirling2).

%F a(n) = (7^n - 8*14^n + 9*21^n)/2.

%F G.f.: 1/Product_{k=1..3} (1 - 7*k*x).

%F E.g.f.: (d^3/dx^3)(((exp(7*x)-1)/7)^3)/3! = (exp(7*x) - 8*exp(14*x) + 9*exp(21*x))/2!.

%Y Cf. A075921, A075923.

%K nonn,easy

%O 0,2

%A _Wolfdieter Lang_, Oct 02 2002