A075922 -id:A075922 - cp's OEIS frontend

A075921 Second column of triangle A075502.

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

Offset: 0

Wolfdieter Lang, Oct 02 2002

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

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

Cf. A000420 (first column), A075922.

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

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

A075923 Fourth column of triangle A075502.

Original entry on oeis.org

1, 70, 3185, 120050, 4084101, 130590390, 4012419145, 120031392250, 3525181576301, 102196720335710, 2935410756419505, 83751552660170850, 2377917929557166101, 67273652916778177030, 1898215473677945050265

Offset: 0

Wolfdieter Lang, Oct 02 2002

The e.g.f. given below is Sum_{m=0..3} A075513(4,m)*exp(7*(m+1)*x)/3!.

Cf. A075922, A075924.

a(n) = A075502(n+4, 4) = (7^n)*S2(n+4, 4) with S2(n, m) := A008277(n, m) (Stirling2).
a(n) = (-7^n + 24*14^n - 81*21^n + 64*28^n)/3!.
G.f.: 1/Product_{k=1..4} (1 - 7*k*x).
E.g.f.: (d^4/dx^4)(((exp(7*x)-1)/7)^4)/4! = (-exp(7*x) + 24*exp(14*x) - 81*exp(21*x) + 64*exp(28*x))/3!.

cp's OEIS Frontend

A075921 Second column of triangle A075502.

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