A075915 Seventh column of triangle A075500.

1, 140, 11550, 735000, 39991875, 1960612500, 89303500000, 3853850000000, 159664583203125, 6409926960937500, 251055710800781250, 9641722822265625000, 364483553427490234375, 13602971247133789062500, 502386213470141601562500, 18394848021467285156250000

Offset

0,2

Comments

The e.g.f. given below is Sum_{m=0..6}(A075513(7,m)exp(5*(m+1)*x))/6!.

Links

Colin Barker, Table of n, a(n) for n = 0..646

Index entries for linear recurrences with constant coefficients, signature (140,-8050,245000,-4230625,41037500,-204187500,393750000).

Formula

a(n) = A075500(n+7, 7) = (5^n)S2(n+7, 7) with S2(n, m) = A008277(n, m) (Stirling2).

a(n) = Sum_{m=0..6}(A075513(7, m)*(5*(m+1))^n)/6!.

G.f.: 1/Product_{k=1..7}(1-5k*x).

E.g.f.: (d^7/dx^7)((((exp(5x)-1)/5)^7)/7!) = (exp(5*x) - 384*exp(10*x) + 10935*exp(15*x) - 81920*exp(20*x) + 234375*exp(25*x) - 279936*exp(30*x) + 117649*exp(35*x))/6!.

G.f.: 1 / ((1-5*x)*(1-10*x)*(1-15*x)*(1-20*x)*(1-25*x)*(1-30*x)*(1-35*x)). - Colin Barker, Dec 12 2015

Mathematica

Table[5^(n-1) * (1 - 3*2^(7 + n) - 5*2^(14 + 2*n) + 5*3^(7 + n) + 3*5^(7 + n) - 6^(7 + n) + 7^(6 + n))/144, {n, 0, 20}] (* Vaclav Kotesovec, Dec 12 2015 *)

Prog

(PARI) Vec(1/((1-5*x)*(1-10*x)*(1-15*x)*(1-20*x)*(1-25*x)*(1-30*x)*(1-35*x)) + O(x^30)) \\ Colin Barker, Dec 12 2015

Crossrefs

Cf. A000351, A016164, A075911, A075912, A075913, A075914.

Sequence in context: A282613 A202786 A035820 * A159362 A188255 A159366

Adjacent sequences: A075912 A075913 A075914 * A075916 A075917 A075918

Keyword

nonn,easy

Author

Wolfdieter Lang, Oct 02 2002

Status

approved