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A133915
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Sum [i=0..n, C(2n-i,n+i)2^i ].
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0
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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; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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).
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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)};
Conjecture: 2*n*a(n) +3*(4-5*n)a(n-1) +6*(4*n-7)*a(n-2) + 8*(2*n-3)*a(n-3)=0. - R. J. Mathar, Nov 14 2011
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CROSSREFS
| Cf. A108081.
Sequence in context: A162551 A073663 A155116 * A150759 A150760 A151303
Adjacent sequences: A133912 A133913 A133914 * A133916 A133917 A133918
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Sep 28 2007
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