A056591 Fifth column sequence of triangle A056588.

1, 12, 166, 1784, 17840, 163504, 1418549, 11751784, 94002810, 730859800, 5554472496, 41437244784, 304478259625, 2209596042260, 15871463933950, 113044318064744, 799558820643440, 5622796403700080, 39354459839661725

Offset: 0

Author

Wolfdieter Lang Jul 10 2000

Keywords

• nonn
• easy

Links

• Robert Israel, Table of n, a(n) for n = 0..1193

Crossrefs

Cf. A000045, A056588, A010048, A000012, A000071, A056589, A056590.

Programs

Maple

g:= (72*x^9-142*x^8+276*x^7+473*x^6-112*x^5-78*x^3+46*x^2-8*x+1)/((1-x)*(1+2*x)*(1-5*x)*(1+x-x^2)*(1+3*x+x^2)*(1-3*x-9*x^2)*(1-4*x-x^2)*(1-6*x+4*x^2) *(1-7*x+x^2)):
S:= series(g,x,21):
seq(coeff(S,x,i),i=0..20); # Robert Israel, Jul 24 2018

Formula

a(n)= A056588(n+4, 4), n >= 0.

a(n)=5^(n+5)-3^(n+5)*F(n+6)-Fibonomial(n+6, 2)*2^(n+5)+Fibonomial(n+6, 3)+Fibonomial(n+6, 4); F(n)=A000045(n) (Fibonacci); Fibonomial(n, m) := A010048(n, m).

G.f.: (72*x^9-142*x^8+276*x^7+473*x^6-112*x^5-78*x^3+46*x^2-8*x+1)/((1-x)*(1+2*x)*(1-5*x)*(1+x-x^2)*(1+3*x+x^2)*(1-3*x-9*x^2)*(1-4*x-x^2)*(1-6*x+4*x^2) *(1-7*x+x^2)).