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Search: id:A135038
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| A135038 |
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Sums of the products of n consecutive quadruples of numbers. |
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+0
1
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| 0, 840, 8760, 41520, 134544, 347064, 768264, 1523424, 2780064, 4754088, 7715928, 11996688, 17994288, 26179608, 37102632, 51398592, 69794112, 93113352, 122284152, 158344176, 202447056, 255868536, 320012616, 396417696, 486762720
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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a(n) = 51.2n^5-32n^4-48n^3+20n^2+8.8n.
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FORMULA
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a(1) = 0*1*2*3 a(2) = 0*1*2*3 + 4*5*6*7 ..., a(n) = 0*1*2*3 + 4*5*6*7 + 8*9*10*11 + ... + (2n-1)*(2n)*(2n+1)(2n+2)
O.g.f.: 24*x^2*(35+155*x+65*x^2+x^3)/(-1+x)^6 . - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 14 2008
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EXAMPLE
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For n = 3, the sum of the first 3 quadruples is 0*1*2*3+4*5*6*7+8*9*10*11 = 8760, the 3rd entry in the sequence.
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MAPLE
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A135038 := proc(n) 20*n^2+44/5*n-48*n^3-32*n^4+256/5*n^5 ; end: seq(A135038(n), n=1..20) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 14 2008
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PROGRAM
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(PARI) sumprod3(n) = { local(x, s=0); forstep(x=0, n, 4, s+=x*(x+1)*(x+2)*(x+3); print1(s", ") ) }
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CROSSREFS
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Adjacent sequences: A135035 A135036 A135037 this_sequence A135039 A135040 A135041
Sequence in context: A092002 A045477 A005952 this_sequence A022052 A055353 A107516
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KEYWORD
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nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)hotmail.com), Feb 11 2008
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