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A121680
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a(n) = [x^n] (1 + x*(1+x)^(n+1) )^(n+1).
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8
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1, 2, 12, 76, 655, 6816, 81690, 1109816, 16782399, 278438740, 5016899833, 97368894756, 2021749249403, 44658312247290, 1044437050070340, 25757381769393392, 667470006331599523, 18119105978249333988
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OFFSET
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0,2
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COMMENTS
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a(n) is divisible by (n+1): a(n)/(n+1) = A121681(n).
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n+1} C(n+1,k) * C((n+1)*k,n-k).
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EXAMPLE
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At n=4, a(4) = [x^4] (1 + x*(1+x)^5 )^5 = 655, since
(1 + x*(1+x)^5 )^5 = 1 + 5*x + 35*x^2 + 160*x^3 + 655*x^4 +...
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MATHEMATICA
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Table[Sum[Binomial[n+1, k] * Binomial[(n+1)*k, n-k], {k, 0, n+1}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 02 2020 *)
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PROG
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(PARI) a(n)=sum(k=0, n+1, binomial(n+1, k)*binomial((n+1)*k, n-k))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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