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A205799
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E.g.f.: exp( Sum_{n>=1} x^(n*(n+1)/2) / (n*(n+1)/2)! ).
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4
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1, 1, 1, 2, 5, 11, 32, 113, 365, 1373, 6072, 25279, 115633, 606321, 3051413, 16344785, 98402881, 576283953, 3523586227, 23840955908, 158428389359, 1085566420290, 8128568533790, 60203101002122, 455911264482697, 3734114950288571, 30413492882578846
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OFFSET
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0,4
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COMMENTS
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Number of set partitions of [n] whose block lengths are triangular numbers. - Alois P. Heinz, Jun 10 2018
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LINKS
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EXAMPLE
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E.g.f.: A(x) = 1 + x + x^2/2! + 2*x^3/3! + 5*x^4/4! + 11*x^5/5! + 32*x^6/6! +...
where
log(A(x)) = x + x^3/3! + x^6/6! + x^10/10! + x^15/15! + x^21/21! +...
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MAPLE
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a:= proc(n) option remember; `if`(n=0, 1, add(`if`(
issqr(8*j+1), a(n-j)*binomial(n-1, j-1), 0), j=1..n))
end:
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MATHEMATICA
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m = 30;
CoefficientList[Exp[Sum[x^(n(n+1)/2)/(n(n+1)/2)!, {n, 1, m}]] + O[x]^m, x]* Range[0, m-1]! (* Jean-François Alcover, Mar 05 2021 *)
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PROG
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(PARI) {a(n)=n!*polcoeff(exp(sum(m=1, sqrtint(2*n+1), x^(m*(m+1)/2)/(m*(m+1)/2)!+x*O(x^n))), n)}
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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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