id:A133915 - OEIS Search Results

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Sum [i=0..n, C(2n-i,n+i)2^i ].

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1, 2, 8, 30, 116, 452, 1772, 6974, 27524, 108852, 431168, 1709996, 6788536, 26971856, 107235668, 426594110, 1697855876, 6760326116, 26927208368, 107288242820, 427596003416, 1704598377176 (list; graph; listen)

	OFFSET	`0,2`
	COMMENT	`A transform of the Jacobsthal numbers A001045(n+1) under the mapping g(x)->(1/(c(x)sqrt(1-4x))g(xc(x)), c(x) the g.f. of A000108. Hankel transform is A001787(n+1).`
	FORMULA	`G.f.: (1-4x+(1-x)sqrt(1-4x))/((x+2)(1-4x)^(3/2)); a(n)=sum{k=0..n, C(2n-k,n+k)2^k}; a(n)=sum{k=0..n, C(n+k-1,k)A001045(n-k+1)};`
	CROSSREFS	`Cf. A108081.` `Sequence in context: A162551 A073663 A155116 this_sequence A150759 A150760 A151303` `Adjacent sequences: A133912 A133913 A133914 this_sequence A133916 A133917 A133918`
	KEYWORD	`easy,nonn`
	AUTHOR	`Paul Barry (pbarry(AT)wit.ie), Sep 28 2007`

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Last modified December 17 23:40 EST 2009. Contains 171025 sequences.

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