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Search: id:A026244
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| 1, 10, 136, 2080, 32896, 524800, 8390656, 134225920, 2147516416, 34359869440, 549756338176, 8796095119360, 140737496743936, 2251799847239680, 36028797153181696, 576460752840294400, 9223372039002259456, 147573952598266347520, 2361183241469182345216
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OFFSET
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0,2
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FORMULA
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With interpolated zeros 0, 1, 0, 10, ... has a(n)=(4^n-(-4)^n+2*2^n-2*(-2)^n)/16 and counts walks of length n between adjacent vertices of the 4-cube. G.f.: (1-10x)/((1-4x)(1-16x)); - Paul Barry (pbarry(AT)wit.ie), Mar 11 2004
a(n)= sum{k=0..n, 9k*binomial(2n,2k)}= sum{k=0..n, 9^k*A086645(n,k)}; a(n)=8^n*T(n,5/4) where T is the Chebyshev polynomial of first kind ; e.g.f.: exp(10x)cosh(6x) . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 08 2009]
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MAPLE
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seq(binomial(-4^n, 2), n=0..18); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 22 2008
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CROSSREFS
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Sequence in context: A128862 A129803 A065024 this_sequence A096619 A003377 A065593
Adjacent sequences: A026241 A026242 A026243 this_sequence A026245 A026246 A026247
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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