A075918 -id:A075918 - cp's OEIS frontend

A075917 Fourth column of triangle A075501.

1, 60, 2340, 75600, 2204496, 60419520, 1591202880, 40800672000, 1027086863616, 25522067450880, 628349082117120, 15366613964083200, 373968813041012736, 9068526888588656640, 219326169845571010560

Offset: 0

Wolfdieter Lang, Oct 02 2002

The e.g.f. given below is Sum_{m=0..3} A075513(4,m)*exp(6*(m+1)*x)/3!.

Cf. A075916, A075918.

a(n) = A075501(n+4, 4) = (6^n)*S2(n+4, 4) with S2(n, m) := A008277(n, m) (Stirling2).
a(n) = Sum_{m=0..3} A075513(4, m)*((m+1)*6)^n/3!.
G.f.: 1/Product_{k=1..4} (1 - 6*k*x).
E.g.f.: (d^4/dx^4)(((exp(6*x)-1)/6)^4)/4! = (-exp(6*x) + 24*exp(12*x) - 81*exp(18*x) + 64*exp(24*x))/3!.

A075919 Sixth column of triangle A075501.

Original entry on oeis.org

1, 126, 9576, 571536, 29583792, 1395690912, 61756307712, 2609370796032, 106548747072768, 4239618914539008, 165370550603102208, 6351034526066700288, 240942052882092847104, 9052126728954680254464

Offset: 0

Wolfdieter Lang, Oct 02 2002

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

Cf. A075918, A075920.

a(n) = A075501(n+6, 6) = (6^n)*S2(n+6, 6) with S2(n, m) := A008277(n, m) (Stirling2).
a(n) = Sum_{m=0..5} A075513(6, m)*((m+1)*6)^n/5!.
G.f.: 1/Product_{k=1..6} (1 - 6*k*x).
E.g.f.: (d^6/dx^6)(((exp(6*x)-1)/6)^6)/6! = (-exp(6*x) + 160*exp(12*x) - 2430*exp(18*x) + 10240*exp(24*x) - 15625*exp(30*x) + 7776*exp(36*x))/5!.

cp's OEIS Frontend

A075917 Fourth column of triangle A075501.

Views

Author

Keywords

Comments

Crossrefs

Formula