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A076004 Fourth column of triangle A075503. 3
1, 80, 4160, 179200, 6967296, 254607360, 8940421120, 305659904000, 10259284361216, 339910422691840, 11158051230842880, 363834840082022400, 11805930580539867136, 381715961976738283520, 12309283295632755261440 (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(8*(m+1)*x)/3!.

LINKS

Michael De Vlieger, Table of n, a(n) for n = 0..663

FORMULA

a(n) = A075503(n+4, 4) = (8^n)*S2(n+4, 4) with S2(n, m) := A008277(n, m) (Stirling2).

a(n) = Sum_{m=0..3} ((A075513(4, m)*(m+1)*8)^n)/3!.

G.f.: 1/Product_{k=1..4} (1 - 8*k*x).

E.g.f.: (d^4/dx^4)(((exp(8*x)-1)/8)^4)/4! = (-exp(8*x) + 24*exp(16*x) - 81*exp(24*x) + 64*exp(32*x))/3!.

MATHEMATICA

With[{m = 4}, Array[8^(# - m) StirlingS2[#, m] &, 15, m]] (* Michael De Vlieger, Dec 24 2017, after Indranil Ghosh at A075503 *)

CROSSREFS

Cf. A076003, A076005.

Sequence in context: A004390 A247861 A203171 * A216987 A283102 A259076

Adjacent sequences:  A076001 A076002 A076003 * A076005 A076006 A076007

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Oct 02 2002

STATUS

approved

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Last modified October 15 23:54 EDT 2019. Contains 328038 sequences. (Running on oeis4.)