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A075507
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Shifts one place left under 8th-order binomial transform.
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6
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1, 1, 9, 89, 1009, 13457, 210105, 3747753, 74565473, 1628999841, 38704241897, 993034281593, 27340167242321, 803154583649329, 25050853217628313, 826165199464341705, 28707262835597618369, 1047731789671001235265, 40053733152627299592137, 1599910554128824794493593
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OFFSET
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0,3
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COMMENTS
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Previous name was: Row sums of triangle A075503 (for n>=1).
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LINKS
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FORMULA
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a(n) = Sum_{m=0..n} 8^(n-m)*S2(n,m), with S2(n,m) = A008277(n,m) (Stirling2).
E.g.f.: exp((exp(8*x)-1)/8).
O.g.f.: Sum_{k>=0} x^k/Product_{j=1..k} (1 - 8*j*x). - Ilya Gutkovskiy, Mar 20 2018
a(n) ~ 8^n * n^n * exp(n/LambertW(8*n) - 1/8 - n) / (sqrt(1 + LambertW(8*n)) * LambertW(8*n)^n). - Vaclav Kotesovec, Jul 15 2021
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MAPLE
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[seq(factorial(k)*coeftayl(exp((exp(8*x)-1)/8), x = 0, k), k=0..20)]; # Muniru A Asiru, Mar 20 2018
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MATHEMATICA
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PROG
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(GAP) List([0..20], n->Sum([0..n], m->8^(n-m)*Stirling2(n, m))); # Muniru A Asiru, Mar 20 2018
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CROSSREFS
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Shifts one place left under k-th order binomial transform, k=1..10: A000110, A004211, A004212, A004213, A005011, A005012, A075506, A075507, A075508, A075509.
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KEYWORD
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nonn,easy,eigen
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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