A075921 Second column of triangle A075502.

1, 21, 343, 5145, 74431, 1058841, 14941423, 210003465, 2945813311, 41281739961, 578226834703, 8097153012585, 113373983463391, 1587332657497881, 22223335428043183, 311131443554114505

Offset: 0

Author

Wolfdieter Lang, Oct 02 2002

Keywords

• nonn
• easy

Comments

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

Links

• Index entries for linear recurrences with constant coefficients, signature (21, -98).

Crossrefs

Cf. A000420 (first column), A075922.

Programs

Mathematica

Table[-7^n+2 14^n,{n,0,20}] (* or *) LinearRecurrence[{21,-98}, {1,21},20] (* Harvey P. Dale, Apr 30 2011 *)

Formula

a(n) = A075502(n+2, 2) = (7^n)*S2(n+2, 2) with S2(n, m) := A008277(n, m) (Stirling2).

a(n) = -7^n + 2*14^n.

G.f.: 1/((1-7*x)*(1-14*x)).

E.g.f.: (d^2/dx^2)(((exp(7*x)-1)/7)^2)/2! = -exp(7*x) + 2*exp(14*x).

a(0)=1, a(1)=21, a(n) = 21a(n-1) - 98a(n-2). - Harvey P. Dale, Apr 30 2011