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

0,2

Links

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

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)).

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

Crossrefs

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

Sequence in context: A193104 A046174 A055760 * A331497 A190063 A160566

Adjacent sequences: A056588 A056589 A056590 * A056592 A056593 A056594

Keyword

nonn,easy

Author

Wolfdieter Lang Jul 10 2000

Status

approved