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Search: id:A121690
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| A121690 |
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G.f.: A(x) = Sum_{k>=0} x^k * (1+x)^(k*(k+1)/2). |
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+0
2
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| 1, 1, 2, 4, 10, 27, 81, 262, 910, 3363, 13150, 54135, 233671, 1053911, 4951997, 24177536, 122381035, 640937746, 3466900453, 19337255086, 111057640382, 655892813805, 3978591077096, 24760700544301, 157941950878839
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OFFSET
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0,3
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FORMULA
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a(n) = Sum_{k=0..n} C(k*(k+1)/2,n-k).
a(n) = A131338(n+1, n*(n+1)/2 + 1) for n>=0, where triangle A131338 starts with a '1' in row 0 and then for n>0 row n consists of n '1's followed by the partial sums of the prior row. - Paul D. Hanna (pauldhanna(AT)juno.com), Aug 30 2007
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PROGRAM
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(PARI) a(n)=sum(k=0, n, binomial(k*(k+1)/2, n-k))
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CROSSREFS
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Cf. A131338.
Adjacent sequences: A121687 A121688 A121689 this_sequence A121691 A121692 A121693
Sequence in context: A114507 A127386 A099950 this_sequence A138356 A057786 A007776
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Aug 15 2006
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