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A016753
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Expansion of 1/((1-3x)(1-4x)(1-5x)).
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2
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1, 12, 97, 660, 4081, 23772, 133057, 724260, 3863761, 20308332, 105558817, 544039860, 2785713841, 14192221692, 72020501377, 364354427460, 1838822866321, 9262446387852, 46585947584737
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OFFSET
| 0,2
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COMMENTS
| As (0,0,1,12,97,...) this is the fourth binomial transform of cosh(x)-1. It is the binomial transform of A016269, when this has two leading zeros. Its e.g.f. is then exp(4x)cosh(x)-exp(4x). - Paul Barry (pbarry(AT)wit.ie), May 13 2003
This gives the third column of the Sheffer triangle A143495 (3-restricted Stirling2 numbers). See the e.g.f. below, and A193685 for comments on the general case. [From Wolfdieter Lang, Oct 08 2011]
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FORMULA
| a(n)=5^(n+2)/2-4^(n+2)+3^(n+2)/2. - Paul Barry (pbarry(AT)wit.ie), May 13 2003
If we define f(m,j,x)=sum(binomial(m,k)*stirling2(k,j)*x^(m-k),k=j..m) then a(n-2)=f(n,2,3), (n>=2). [From Milan R. Janjic (agnus(AT)blic.net), Apr 26 2009]
a(n) = 9*a(n-1) -20*a(n-2) +3^n, n>=2. - Vincenzo Librandi, Mar 20 2011
O.g.f.:1/((1-3*x)*(1-4*x)*(1-5*x)).
E.g.f.: diff(exp(3*x)*((exp(x)-1)^2)/2!,x$2). [From Wolfdieter Lang, Oct 08 2011]
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MATHEMATICA
| CoefficientList[ Series[ 1/((1 - 3x)(1 - 4x)(1 - 5x)), {x, 0, 25} ], x ]
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CROSSREFS
| A000244, A00506, A016753.
Sequence in context: A059375 A027255 A121791 * A078605 A021029 A128594
Adjacent sequences: A016750 A016751 A016752 * A016754 A016755 A016756
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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