A380042
E.g.f. A(x) satisfies A(x) = 1/sqrt( 1 - 2*x*exp(x*A(x)^2) ).
Original entry on oeis.org
1, 1, 5, 48, 697, 13640, 336771, 10053778, 352334753, 14183529480, 645073504435, 32715111226886, 1830671281889649, 112049330303532388, 7446824171300128811, 534068807341887943770, 41111698162393482004801, 3381089519620006418116976, 295869084136630532211207843
Offset: 0
-
my(N=20, x='x+O('x^N)); Vec(serlaplace(sqrt(serreverse(x/(1+2*x*exp(x)))/x)))
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a(n) = n!*sum(k=0, n, 2^k*k^(n-k)*binomial(n+1/2, k)/(n-k)!)/(2*n+1);
A380093
E.g.f. A(x) satisfies A(x) = sqrt( 1 + 2*x*exp(x*A(x)) ).
Original entry on oeis.org
1, 1, 1, 6, 13, 180, 501, 13720, 34777, 2014992, 2512585, 491642976, -564313947, 181714012480, -836832558275, 95473740036480, -856984734161999, 68029327826567424, -954950936641491951, 63368301861354866176, -1238053892876418633155, 74904417332353810338816
Offset: 0
A380077
Expansion of e.g.f. (1/x) * Series_Reversion( x * sqrt(1 - 2*x*exp(x)) ).
Original entry on oeis.org
1, 1, 7, 87, 1621, 40485, 1271841, 48220207, 2143450009, 109350344745, 6298638659245, 404371344546411, 28633701543626037, 2217105596852342989, 186362307297569836993, 16901012222196104542695, 1644911203243501609414321, 171017059743998995011125457, 18916512667390427993433246357
Offset: 0
-
my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*sqrt(1-2*x*exp(x)))/x))
-
a(n) = n!*sum(k=0, n, 2^k*k^(n-k)*binomial(n/2+k+1/2, k)/((n+2*k+1)*(n-k)!));
Showing 1-3 of 3 results.