A373578
Expansion of e.g.f. exp(x * (1 + x^2)^2).
Original entry on oeis.org
1, 1, 1, 13, 49, 241, 2401, 13021, 128353, 1346689, 10615681, 140431501, 1544877841, 17576665393, 264566466529, 3226728670621, 48376006929601, 766753039205761, 11052669865900033, 197019825098096269, 3271213100827557361, 56597110823949654001
Offset: 0
-
nmax = 20; CoefficientList[Series[E^(x*(1 + x^2)^2), {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Jun 11 2024 *)
-
a(n) = n!*sum(k=0, 2*n\5, binomial(2*n-4*k, k)/(n-2*k)!);
A012150
Expansion of e.g.f. exp(tan(arcsin(x))).
Original entry on oeis.org
1, 1, 1, 4, 13, 76, 421, 3256, 25369, 245008, 2449801, 28441216, 346065061, 4700478784, 67243537453, 1047088053376, 17192488230961, 302112622479616, 5593309059948049, 109527844826856448, 2255588021494237501
Offset: 0
Patrick Demichel (patrick.demichel(AT)hp.com)
exp(tan(arcsin(x))) = 1+x+1/2!*x^2+4/3!*x^3+13/4!*x^4+76/5!*x^5...
-
A012150 := proc(n) if n = 0 then 1; else add( (1+(-1)^(n-k)) *binomial((n-2)/2,(n-k)/2)/(2*k!), k=1..n) ; %*n! ; end if; end proc: # R. J. Mathar, Mar 20 2011
-
Range[0, 20]! CoefficientList[Series[Exp[Tan[ArcSin[x]]], {x, 0, 20}], x] (* Or *)
f[n_] := n! Sum[(1 + (-1)^(n - k)) Binomial[(n - 2)/2, (n - k)/2]/2/k!, {k, n}]; f[0] = 1; Array[f, 21, 0] (* Robert G. Wilson v, Feb 19 2011 *)
-
my(x='x+O('x^30)); Vec(serlaplace(exp(tan(asin(x))))) \\ Michel Marcus, Oct 30 2022
A373577
Expansion of e.g.f. exp(x * (1 + x^2)^(3/2)).
Original entry on oeis.org
1, 1, 1, 10, 37, 136, 1261, 6616, 45865, 479872, 3206521, 31165696, 356045581, 3082798720, 37528974757, 443190912256, 4792765859281, 69943918698496, 875123733523825, 11059833224507392, 179428023035501941, 2557848382674927616, 37699048392962570461
Offset: 0
A373542
Expansion of e.g.f. exp(x * sqrt(1-x^2)).
Original entry on oeis.org
1, 1, 1, -2, -11, -44, -59, -104, 1513, -4976, 14761, -1005344, -594659, -120135872, -8409491, -19661062784, 461914321, -4406419844864, 8555830993, -1268264427577856, -595229416379, -455779307821067264, -13631036685419, -200172063313066452992
Offset: 0
Showing 1-4 of 4 results.