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A193437
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E.g.f.: exp( Sum_{n>=0} x^(3*n+1)/(3*n+1) ).
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2
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1, 1, 1, 1, 7, 31, 91, 931, 7441, 38017, 507241, 5864761, 43501591, 713059711, 10776989587, 105784464331, 2052437475361, 38263122487681, 469863736958161, 10518597616325617, 232980391759702951, 3446848352553524191, 87385257330831947851
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OFFSET
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0,5
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COMMENTS
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Conjecture: a(n) is divisible by 7^floor(n/7) for n>=0.
Conjecture: a(n) is divisible by p^floor(n/p) for prime p == 1 (mod 3).
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LINKS
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Table of n, a(n) for n=0..22.
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FORMULA
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a(n) = a(n-1) + (n-3)*(n-2)*(n-1)*a(n-3). - Vaclav Kotesovec, Apr 15 2020
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EXAMPLE
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E.g.f.: A(x) = 1 + x + x^2/2! + x^3/3! + 7*x^4/4! + 31*x^5/5! + 91*x^6/6! + 931*x^7/7! +...
where
log(A(x)) = x + x^4/4 + x^7/7 + x^10/10 + x^13/13 + x^16/16 + x^19/19 +...
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MATHEMATICA
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nmax = 30; CoefficientList[Series[Exp[x*Hypergeometric2F1[1/3, 1, 4/3, x^3]], {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Apr 15 2020 *)
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PROG
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(PARI) {a(n)=n!*polcoeff( exp(sum(m=0, n, x^(3*m+1)/(3*m+1))+x*O(x^n)) , n)}
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CROSSREFS
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Cf. A000246, A193438.
Sequence in context: A118935 A226838 A205801 * A199921 A192596 A055899
Adjacent sequences: A193434 A193435 A193436 * A193438 A193439 A193440
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna, Jul 25 2011
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STATUS
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approved
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