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Search: id:A051747
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| A051747 |
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a(n)=(1/120)*n*(n+1)*(n+2)*(n^2+7*n+32). |
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+0
4
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| 2, 10, 31, 76, 161, 308, 546, 912, 1452, 2222, 3289, 4732, 6643, 9128, 12308, 16320, 21318, 27474, 34979, 44044, 54901, 67804, 83030, 100880, 121680, 145782, 173565, 205436, 241831, 283216, 330088, 382976, 442442, 509082, 583527, 666444, 758537
(list; graph; listen)
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OFFSET
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1,1
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FORMULA
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a(n)=binomial(n+4, n-1)+binomial(n+2, n-1)
Convolution of triangular numbers with triangular numbers + 1, i.e. [1, 3, 6, 10, 15, 21, ...] with [2, 4, 7, 11, 16, 22, ...]
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PROGRAM
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(PARI) conv(u, v)=local(w); w=vector(length(u), i, sum(j=1, i, u[j]*v[i+1-j])); w; t(n)=n*(n+1)/2; u=vector(10, i, t(i)); v=vector(10, i, t(i)+1); conv(u, v)
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CROSSREFS
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Cf. A000217, A000389, A005583.
Sequence in context: A162249 A156492 A090809 this_sequence A024456 A050927 A011921
Adjacent sequences: A051744 A051745 A051746 this_sequence A051748 A051749 A051750
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KEYWORD
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easy,nonn
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AUTHOR
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Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 07 1999
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