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A084137
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Binomial transform of A084136.
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1
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1, 2, 8, 32, 144, 672, 3200, 15360, 73984, 356864, 1722368, 8314880, 40144896, 193830912, 935886848, 4518838272, 21818834944, 105350561792, 508677324800, 2456111022080, 11859152338944, 57261051346944, 276480810549248
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(n)=(A084128(n)+2^n)/2.
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FORMULA
| G.f.: (1-4x)/((1-2x)(1-4x-4x^2)). E.g.f.: exp(2x)cosh(sqrt(2)x)^2=(exp(x)cosh(sqrt(2)x))^2. a(n)=(2+sqrt(8))^n/4+(2-sqrt(8))^n/4+2^n/2.
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PROG
| (PARI) a(n)=if(n<0, 0, polsym(4+4*x-x^2, n)[n+1]/4+2^(n-1))
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CROSSREFS
| Sequence in context: A150861 A150862 A150863 * A129400 A003304 A150864
Adjacent sequences: A084134 A084135 A084136 * A084138 A084139 A084140
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), May 16 2003
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