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)!.

1, 2, 20, 504, 23968, 1851520, 211575936, 33566973440, 7062343608320, 1903365244784640, 639521861269258240, 262112584945787699200, 128722417690687207833600, 74622047155540651999232000, 50422787106606997974155264000, 39283625022760603948312795545600, 34956170646455883939814603698995200, 35235028408984566235493250881290240000, 39938723513704723231184585043746173747200

Offset

1,2

Links

Table of n, a(n) for n=1..19.

Example

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! +...
such that
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) +...

Prog

(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)}
for(n=1, 25, print1(a(n), ", "))

Crossrefs

Sequence in context: A279839 A279837 A279200 * A296789 A168136 A103353

Adjacent sequences: A277411 A277412 A277413 * A277415 A277416 A277417

Keyword

nonn

Author

Paul D. Hanna, Nov 17 2016

Status

approved