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 A193437 E.g.f.: exp( Sum_{n>=0} x^(3*n+1)/(3*n+1) ). 1

%I

%S 1,1,1,1,7,31,91,931,7441,38017,507241,5864761,43501591,713059711,

%T 10776989587,105784464331,2052437475361,38263122487681,

%U 469863736958161,10518597616325617,232980391759702951,3446848352553524191,87385257330831947851

%N E.g.f.: exp( Sum_{n>=0} x^(3*n+1)/(3*n+1) ).

%C Conjecture: a(n) is divisible by 7^floor(n/7) for n>=0.

%C Conjecture: a(n) is divisible by p^floor(n/p) for prime p == 1 (mod 3).

%e 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! +...

%e where

%e log(A(x)) = x + x^4/4 + x^7/7 + x^10/10 + x^13/13 + x^16/16 + x^19/19 +...

%o (PARI) {a(n)=n!*polcoeff( exp(sum(m=0,n,x^(3*m+1)/(3*m+1))+x*O(x^n)) ,n)}

%Y Cf. A193438.

%K nonn

%O 0,5

%A _Paul D. Hanna_, Jul 25 2011

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Last modified February 21 23:21 EST 2020. Contains 332113 sequences. (Running on oeis4.)