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A075907 Fourth column of triangle A075499. 3
1, 40, 1040, 22400, 435456, 7956480, 139694080, 2387968000, 40075329536, 663887544320, 10896534405120, 177653730508800, 2882307270639616, 46596186764738560, 751299029274460160, 12089975328525516800 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (40, -560, 3200, -6144).

FORMULA

a(n) = A075499(n+4, 4) = (4^n)*S2(n+4, 4) with S2(n, m) := A008277(n, m) (Stirling2).

a(n) = (-4^n + 24*8^n - 81*12^n + 64*16^n)/3!.

G.f.: 1/Product_{k=1..4} (1 - 4*k*x).

E.g.f.: (d^4/dx^4)(((exp(4*x)-1)/4)^4)/4! = (-exp(4*x) + 24*exp(8*x) - 81*exp(12*x) + 64*exp(16*x))/3!.

a(0)=1, a(1)=40, a(2)=1040, a(3)=22400, a(n) = 40*a(n-1) - 560*a(n-2) + 3200*a(n-3) - 6144*a(n-4). - Harvey P. Dale, Jun 04 2013

MATHEMATICA

Table[(-4^n+24*8^n-81*12^n+64*16^n)/6, {n, 0, 20}] (* or *) LinearRecurrence[ {40, -560, 3200, -6144}, {1, 40, 1040, 22400}, 20] (* Harvey P. Dale, Jun 04 2013 *)

CROSSREFS

Cf. A019677, A075908.

Sequence in context: A016092 A028228 A165380 * A062143 A284838 A124100

Adjacent sequences:  A075904 A075905 A075906 * A075908 A075909 A075910

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Oct 02 2002

STATUS

approved

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Last modified April 5 20:18 EDT 2020. Contains 333260 sequences. (Running on oeis4.)