A377827
E.g.f. satisfies A(x) = (1 + x)^2 * exp(x * A(x)).
Original entry on oeis.org
1, 3, 13, 106, 1273, 20226, 402589, 9637902, 269967793, 8666441650, 313793596981, 12653878751526, 562489374836041, 27328756018660266, 1440892788988703821, 81940739770677315646, 4999648556871348611425, 325806859913842861709922, 22584652022005415601772645
Offset: 0
A376145
E.g.f. satisfies A(x) = exp( x * (1+x)^3 * A(x) ).
Original entry on oeis.org
1, 1, 9, 88, 1265, 23916, 558427, 15608986, 508516017, 18936594712, 793902926771, 37017671474334, 1900666877186761, 106576903636156084, 6481047448001720427, 424870924596413523106, 29871349825140536394593, 2242231079099137007066544
Offset: 0
A378019
E.g.f. satisfies A(x) = (1+x) * exp( x * (1+x) * A(x) ).
Original entry on oeis.org
1, 2, 9, 79, 957, 15441, 309943, 7468301, 210221385, 6774449185, 246049105131, 9947338595085, 443121311695021, 21568178966624993, 1138938283455953919, 64856665518838006861, 3961941908569940501649, 258453847468153873181889, 17932482767578645884498643
Offset: 0
-
my(N=20, x='x+O('x^N)); Vec(serlaplace((1+x)*exp(-lambertw(-x*(1+x)^2))))
-
a(n) = n!*sum(k=0, n, (k+1)^(k-1)*binomial(2*k+1, n-k)/k!);
A362774
E.g.f. satisfies A(x) = exp( x * (1+x)^2 * A(x)^2 ).
Original entry on oeis.org
1, 1, 9, 115, 2265, 59701, 1981513, 79441167, 3736418801, 201790517833, 12309193580841, 837132560820139, 62809405894333321, 5154060532188515325, 459202970647825870313, 44146740571635016905991, 4555272678073789024849377, 502153774773932684443210513
Offset: 0
-
A362774 := proc(n)
n!*add((2*k+1)^(k-1) * binomial(2*k,n-k)/k!,k=0..n) ;
end proc:
seq(A362774(n),n=0..70) ; # R. J. Mathar, Dec 04 2023
-
my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-2*x*(1+x)^2)/2)))
A376146
E.g.f. satisfies A(x) = exp( x * (1+x)^4 * A(x) ).
Original entry on oeis.org
1, 1, 11, 124, 1997, 42616, 1120327, 35203960, 1288741337, 53898829408, 2536932089771, 132770439164584, 7649993702503429, 481295935534882768, 32834728249861856879, 2414570451161244199576, 190412665638185073399473, 16030575396743899522805440
Offset: 0
Showing 1-5 of 5 results.