A075921 Second column of triangle A075502.

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

Offset

0,2

Comments

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

Links

Table of n, a(n) for n=0..15.

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

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

Mathematica

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

Crossrefs

Cf. A000420 (first column), A075922.

Sequence in context: A144864 A295604 A323277 * A201878 A318269 A298229

Adjacent sequences: A075918 A075919 A075920 * A075922 A075923 A075924

Keyword

nonn,easy

Author

Wolfdieter Lang, Oct 02 2002

Status

approved