A363509
G.f. satisfies A(x) = exp( Sum_{k>=1} (-1)^(k+1) * (3 + A(x^k)) * x^k/k ).
Original entry on oeis.org
1, 4, 10, 30, 101, 361, 1354, 5238, 20740, 83683, 342719, 1421019, 5953306, 25162342, 107163924, 459438524, 1981247950, 8588054014, 37398421941, 163534601567, 717776072291, 3161117717887, 13964782042188, 61866495037806, 274792382789958
Offset: 0
-
terms = 25; A[] = 0; Do[A[x] = Exp[Sum[(-1)^(k+1)*(3+A[x^k])*x^k/k,{k,terms}]]+ O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* Stefano Spezia, May 10 2025 *)
-
seq(n) = my(A=1); for(i=1, n, A=exp(sum(k=1, i, (-1)^(k+1)*(3+subst(A, x, x^k))*x^k/k)+x*O(x^n))); Vec(A);
A038076
Number of rooted identity trees with 3-colored leaves.
Original entry on oeis.org
3, 3, 6, 16, 46, 142, 461, 1542, 5278, 18417, 65218, 233816, 846938, 3094943, 11395715, 42237936, 157465847, 590075550, 2221391912, 8397223487, 31861406058, 121300625969, 463233477550, 1774034788166, 6811612470692, 26216538077715, 101125406981562
Offset: 1
-
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(binomial(a(i$2), j)*b(n-i*j, i-1), j=0..n/i)))
end:
a:= n-> `if`(n<2, 3*n, b(n-1, n-1)):
seq(a(n), n=1..35); # Alois P. Heinz, Aug 01 2013
-
b[n_, i_] := b[n, i] = If[n==0, 1, If[i<1, 0, Sum[Binomial[a[i], j]*b[n - i*j, i-1], {j, 0, n/i}]]];
a[n_] := If[n<2, 3*n, b[n-1, n-1]];
Table[a[n], {n, 1, 35}] (* Jean-François Alcover, Mar 01 2016, after Alois P. Heinz *)
A031148
Number of series-reduced planted trees with n leaves of 2 colors and no symmetries.
Original entry on oeis.org
2, 1, 2, 5, 14, 43, 138, 455, 1540, 5305, 18546, 65616, 234546, 845683, 3072350, 11235393, 41326470, 152793376, 567518950, 2116666670, 7924062430, 29765741831, 112157686170, 423809991041, 1605622028100
Offset: 1
A363510
G.f. satisfies A(x) = exp( Sum_{k>=1} (-1)^(k+1) * (4 + A(x^k)) * x^k/k ).
Original entry on oeis.org
1, 5, 15, 50, 190, 766, 3231, 14066, 62681, 284591, 1311622, 6120183, 28855529, 137257541, 657894518, 3174411715, 15406640415, 75162477018, 368383443235, 1813007892858, 8956214966017, 44393932344984, 220732441125743, 1100621484436502
Offset: 0
-
seq(n) = my(A=1); for(i=1, n, A=exp(sum(k=1, i, (-1)^(k+1)*(4+subst(A, x, x^k))*x^k/k)+x*O(x^n))); Vec(A);
A363542
G.f. satisfies A(x) = exp( Sum_{k>=1} (-1)^(k+1) * (2^k + A(x^k)) * x^k/k ).
Original entry on oeis.org
1, 3, 5, 14, 38, 114, 360, 1166, 3872, 13094, 44961, 156244, 548636, 1943333, 6935817, 24917586, 90039163, 327029681, 1193258619, 4371901789, 16077606949, 59325057056, 219579151797, 815017718383, 3032959638204, 11313632991360, 42295634914403
Offset: 0
-
seq(n) = my(A=1); for(i=1, n, A=exp(sum(k=1, i, (-1)^(k+1)*(2^k+subst(A, x, x^k))*x^k/k)+x*O(x^n))); Vec(A);
A363543
G.f. satisfies A(x) = exp( Sum_{k>=1} (-1)^(k+1) * (3^k + A(x^k)) * x^k/k ).
Original entry on oeis.org
1, 4, 7, 23, 69, 234, 826, 3000, 11168, 42313, 162829, 634052, 2495051, 9903761, 39612048, 159481988, 645833656, 2628829700, 10749777653, 44139474552, 181916530895, 752288709592, 3120574260606, 12981015704961, 54138655342763, 226330448292140
Offset: 0
-
seq(n) = my(A=1); for(i=1, n, A=exp(sum(k=1, i, (-1)^(k+1)*(3^k+subst(A, x, x^k))*x^k/k)+x*O(x^n))); Vec(A);
Showing 1-6 of 6 results.