A076005 -id:A076005 - cp's OEIS frontend

A076004 Fourth column of triangle A075503.

1, 80, 4160, 179200, 6967296, 254607360, 8940421120, 305659904000, 10259284361216, 339910422691840, 11158051230842880, 363834840082022400, 11805930580539867136, 381715961976738283520, 12309283295632755261440

Offset: 0

Wolfdieter Lang, Oct 02 2002

The e.g.f. given below is Sum_{m=0..3} A075513(4,m)*exp(8*(m+1)*x)/3!.

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

Cf. A076003, A076005.

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

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!.

A076006 Sixth column of triangle A075503.

Original entry on oeis.org

1, 168, 17024, 1354752, 93499392, 5881430016, 346987429888, 19548208103424, 1064285732077568, 56464495286943744, 2936605030892961792, 150373246607730671616, 7606369972746352328704, 381025640076812853706752

Offset: 0

Wolfdieter Lang, Oct 02 2002

The e.g.f. given below is Sum_{m=0..5} (A075513(6,m)*exp(8*(m+1)*x))/5!.

Michael De Vlieger, Table of n, a(n) for n = 0..593

Cf. A076005, A076007.

With[{m = 6}, Array[8^(# - m) StirlingS2[#, m] &, 14, m]] (* Michael De Vlieger, Dec 24 2017, after Indranil Ghosh at A075503 *)

a(n) = A075503(n+6, 6) = (8^n)*S2(n+6, 6) with S2(n, m) := A008277(n, m) (Stirling2).
a(n) = Sum_{m=0..5} (A075513(6, m)*((m+1)*8)^n)/5!.
G.f.: 1/Product_{k=1..6} (1 - 8*k*x).
E.g.f.: (d^6/dx^6)(((exp(8*x)-1)/8)^6)/6! = (-exp(8*x) + 160*exp(16*x) - 2430*exp(24*x) + 10240*exp(32*x) - 15625*exp(40*x) + 7776*exp(48*x))/5!.

cp's OEIS Frontend

A076004 Fourth column of triangle A075503.

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