id:A105695 - OEIS Search Results

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Expansion of (1-x)c(x/(1+x)), c(x) the g.f. of the Catalan numbers A000108.

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1, 0, 0, 1, 2, 5, 12, 30, 76, 196, 512, 1353, 3610, 9713, 26324, 71799, 196938, 542895, 1503312, 4179603, 11662902, 32652735, 91695540, 258215664, 728997192, 2062967382, 5850674704, 16626415975, 47337954326 (list; graph; listen)

	OFFSET	`0,5`
	COMMENT	`Apply the Riordan array (1-x,x/(1+x)) to C(n)=A000108(n).`
	FORMULA	`G.f.: (1-x^2)(1-sqrt((1-3x)/(1+x)))/(2x); Let b(n)=sum{k=0..n, (-1)^(n-k)binomial(n, k)C(k)}=A005043(n); then a(n)=b(n)-b(n-2).`
	CROSSREFS	`Cf. A002026.` `Sequence in context: A051450 A038508 A002026 this_sequence A026938 A086622 A024851` `Adjacent sequences: A105692 A105693 A105694 this_sequence A105696 A105697 A105698`
	KEYWORD	`easy,nonn`
	AUTHOR	`Paul Barry (pbarry(AT)wit.ie), Apr 17 2005`

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Last modified December 16 17:18 EST 2009. Contains 170825 sequences.

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