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A193933
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E.g.f. A(x) = exp(x+x^2+x^3+x^4+x^5+x^6+x^7).
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2
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1, 1, 3, 13, 73, 501, 4051, 37633, 354033, 3870793, 46240291, 597877941, 8298856633, 122751616573, 1921371570483, 31604885804521, 552755907700321, 10156326950561553, 195421314725788483, 3926668816722630493, 82199760488718697641, 1789438454541407131141
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OFFSET
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0,3
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LINKS
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FORMULA
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E.g.f.: exp(Sum_{j=1..7} x^j).
a(n) = n!*sum(k=1..n, sum(i=0..(n-k)/7, (-1)^i*binomial(k,k-i)*binomial(n-7*i-1,k-1))/k!), n>0, a(0)=1.
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MAPLE
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a:= proc(n) option remember; `if`(n=0, 1, add(
a(n-j)*binomial(n-1, j-1)*j!, j=1..min(n, 7)))
end:
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MATHEMATICA
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terms = 22;
CoefficientList[E^Total[x^Range[7]] + O[x]^terms, x] Range[0, terms-1]! (* Jean-François Alcover, Nov 11 2020 *)
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PROG
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(Maxima)
a(n):=if n=0 then 1 else n!*sum(sum((-1)^i*binomial(k, k-i)*binomial(n-7*i-1, k-1), i, 0, (n-k)/7)/k!, k, 1, n);
makelist(a(n), n, 0, 20);
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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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