A118192 - OEIS

This site is supported by donations to The OEIS Foundation.

A118192

Antidiagonal sums of triangle A118190: a(n) = Sum_{k=0..[n/2]} (5^k)^(n-2*k) for n>=0.

1, 1, 2, 6, 27, 151, 1252, 18876, 421877, 11797501, 489062502, 36867190626, 4119892578127, 576049853531251, 119400024902343752, 45003894807128984376, 25145828723919677734377, 17579646409034759521875001 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`0,3`
	LINKS	`Table of n, a(n) for n=0..17.`
	FORMULA	`G.f.: A(x) = Sum_{n>=0} x^n/(1-5^nx^2). a(2n) = Sum_{k=0..n} (5^k)^(2(n-k)); a(2*n+1) = Sum_{k=0..n} (5^k)^(2(n-k)+1).`
	EXAMPLE	`A(x) = 1/(1-x^2) + x/(1-5x^2) + x^2/(1-25x^2) + x^3/(1-125x^2) +...` `= 1 + x + 2x^2 + 6x^3 + 27x^4 + 151x^5 +...`
	PROG	`(PARI) a(n)=sum(k=0, n\2, (5^k)^(n-2*k) )`
	CROSSREFS	`Cf. A118190 (triangle), A118191 (row sums).` `Sequence in context: A030967 A030858 A030932 * A058133 A009308 A032186` `Adjacent sequences: A118189 A118190 A118191 * A118193 A118194 A118195`
	KEYWORD	`nonn`
	AUTHOR	`Paul D. Hanna, Apr 15 2006`
	STATUS	`approved`

Content is available under The OEIS End-User License Agreement .

Last modified May 19 23:59 EDT 2013. Contains 225436 sequences.