id:A112478 - OEIS Search Results

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Expansion of (1+x+sqrt(1+6x+x^2))/2.

+0
4

1, 2, -2, 6, -22, 90, -394, 1806, -8558, 41586, -206098, 1037718, -5293446, 27297738, -142078746, 745387038, -3937603038, 20927156706, -111818026018, 600318853926, -3236724317174, 17518619320890, -95149655201962, 518431875418926, -2832923350929742, 15521467648875090 (list; graph; listen)

	OFFSET	`0,2`
	COMMENT	`This is the A-sequence for the Delannoy triangle A008288. See the W. Lang link under A006232 for Sheffer a- and z-sequences where also Riordan A- and Z-sequences are explained. O.g.f. A(y)=y/Finv(y) = 2y/(-(1+y)+sqrt(y^2+6y+1)) = ((1+y)+sqrt(1+6y+y^2))/2 with Finv the inverse function of F(x)=x(1+x)/(1-x). The o.g.f. of the Z-sequence is 1.`
	CROSSREFS	`A minor variation of A006318. Cf. A085403.` `Row sums of number triangle A112477.` `Adjacent sequences: A112475 A112476 A112477 this_sequence A112479 A112480 A112481` `Sequence in context: A007985 A097090 A085403 this_sequence A138801 A069466 A076741`
	KEYWORD	`easy,sign`
	AUTHOR	`Paul Barry (pbarry(AT)wit.ie), Sep 07 2005`

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Last modified October 11 13:47 EDT 2008. Contains 144830 sequences.

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