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 A277414 E.g.f.: Series_Reversion( Sum_{n>=1} (-1)^(n-1) * x^(2*n-1)/(n*(n+1)/2) ) = Sum_{n>=1} a(n)*x^(2*n-1)/(2*n-1)!. 0

%I #3 Nov 17 2016 01:07:27

%S 1,2,20,504,23968,1851520,211575936,33566973440,7062343608320,

%T 1903365244784640,639521861269258240,262112584945787699200,

%U 128722417690687207833600,74622047155540651999232000,50422787106606997974155264000,39283625022760603948312795545600,34956170646455883939814603698995200,35235028408984566235493250881290240000,39938723513704723231184585043746173747200

%N E.g.f.: Series_Reversion( Sum_{n>=1} (-1)^(n-1) * x^(2*n-1)/(n*(n+1)/2) ) = Sum_{n>=1} a(n)*x^(2*n-1)/(2*n-1)!.

%e E.g.f.: A(x) = x + 2*x^3/3! + 20*x^5/5! + 504*x^7/7! + 23968*x^9/9! + 1851520*x^11/11! + 211575936*x^13/13! + 33566973440*x^15/15! +...

%e such that

%e Series_Reversion(A(x)) = x - x^3/3 + x^5/6 - x^7/10 + x^9/15 - x^11/21 + x^13/28 +...+ (-1)^(n-1)*x^(2*n-1)/(n*(n+1)/2) +...

%o (PARI) {a(n) = (2*n-1)! * polcoeff( serreverse( sum(m=1, n, (-1)^(m-1) * x^(2*m-1) / (m*(m+1)/2) ) +O(x^(2*n+2))), 2*n-1)}

%o for(n=1,25,print1(a(n),", "))

%K nonn

%O 1,2

%A _Paul D. Hanna_, Nov 17 2016

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Last modified June 6 22:19 EDT 2023. Contains 363151 sequences. (Running on oeis4.)