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A118193 Column 0 of the matrix inverse of triangle A118190(n,k) = (5^k)^(n-k). 3
1, -1, 4, -76, 7124, -3326876, 7760553124, -90490361296876, 5275336666748203124, -1537656615631182860546876, 2240970675863910673065189453124, -16329855533286908545970966339091796876, 594974481262862479448134839533519744970703124 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The entire matrix inverse of triangle A118193 is determined by column 0 (this sequence): [A118190^-1](n,k) = a(n-k)*(5^k)^(n-k) for n>=k>=0. Any g.f. of the form: Sum_{k>=0} b(k)*x^k may be expressed as: Sum_{n>=0} c(n)*x^n/(1-5^n*x) by applying the inverse transformation: c(n) = Sum_{k=0..n} a(n-k)*b(k)*(5^k)^(n-k).

LINKS

Table of n, a(n) for n=0..12.

FORMULA

G.f.: 1 = Sum_{n>=0} a(n)*x^n/(1-5^n*x). 0^n = Sum_{k=0..n} a(k)*(5^k)^(n-k) for n>=0.

EXAMPLE

Recurrence at n=4:

0 = a(0)*(5^0)^4 +a(1)*(5^1)^3 +a(2)*(5^2)^2 +a(3)*(5^3)^1 +a(4)*(5^4)^0

= 1*(5^0) - 1*(5^3) + 4*(5^4) - 76*(5^3) + 7124*(5^0).

The g.f. is illustrated by:

1 = 1/(1-x) - 1*x/(1-5*x) + 4*x^2/(1-25*x) - 76*x^3/(1-125*x) +

7124*x^4/(1-625*x) - 3326876*x^5/(1-3125*x) + 7760553124*x^6/(1-15625*x) +...

PROG

(PARI) {a(n)=local(T=matrix(n+1, n+1, r, c, if(r>=c, (5^(c-1))^(r-c)))); return((T^-1)[n+1, 1])}

CROSSREFS

Cf. A118190.

Sequence in context: A012010 A012155 A325214 * A052271 A184272 A080989

Adjacent sequences:  A118190 A118191 A118192 * A118194 A118195 A118196

KEYWORD

sign

AUTHOR

Paul D. Hanna, Apr 15 2006

STATUS

approved

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Last modified May 23 07:08 EDT 2019. Contains 323508 sequences. (Running on oeis4.)