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A215979 Number of simple unlabeled graphs on 2*n nodes with exactly n connected components that are trees or cycles. 2
1, 1, 3, 6, 13, 26, 56, 115, 247, 533, 1175, 2636, 6040, 14078, 33401, 80524, 196897, 487781, 1222279, 3094507, 7905992, 20364597, 52838720, 138001953, 362565398, 957687474, 2542056376, 6777855755, 18146153182, 48766704695, 131517773945, 355842838357 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Limiting sequence of reversed rows of A215977.  Also central elements of rows of A215977.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..200

FORMULA

a(n) = A215977(2*n,n).

a(n) ~ c * d^n / n^(5/2), where d = A051491 = 2.9557652856..., c = 4.034813602... . - Vaclav Kotesovec, Aug 31 2014

EXAMPLE

a(3) = 6: .o-o o.  .o-o o.  .o-o o.  .o-o o.  .o-o o.  .o o o.

          .| |  .  .|    .  .|\   .  .|/   .  .|    .  .| | |.

          .o-o o.  .o-o o.  .o o o.  .o o-o.  .o o-o.  .o o o.

MAPLE

with(numtheory):

b:= proc(n) option remember; local d, j; `if`(n<=1, n,

      (add(add(d*b(d), d=divisors(j)) *b(n-j), j=1..n-1))/(n-1))

    end:

g:= proc(n) option remember; local k; `if`(n>2, 1, 0)+ b(n)-

      (add(b(k)*b(n-k), k=0..n) -`if`(irem(n, 2)=0, b(n/2), 0))/2

    end:

p:= proc(n, i, t) option remember; `if`(n<t, 0, `if`(n=t, 1,

      `if`(min(i, t)<1, 0, add(binomial(g(i)+j-1, j)*

       p(n-i*j, i-1, t-j), j=0..min(n/i, t)))))

    end:

a:= n-> p(2*n, 2*n, n):

seq(a(n), n=0..35);

MATHEMATICA

b[n_] := b[n] = If[n <= 1, n, (Sum[DivisorSum[j, #*b[#]&]*b[n-j], {j, 1, n-1}])/(n-1)];

g[n_] := g[n] = If[n > 2, 1, 0] + b[n] - (Sum[b[k]*b[n-k], {k, 0, n}] - If[EvenQ[n], b[n/2], 0])/2;

p[n_, i_, t_] := p[n, i, t] = If[n < t, 0, If[n == t, 1, If[Min[i, t]<1, 0, Sum[Binomial[g[i]+j-1, j]*p[n-i*j, i-1, t-j], {j, 0, Min[n/i, t]}]]]];

a[n_] := p[2*n, 2*n, n];

Table[a[n], {n, 0, 35}] (* Jean-Fran├žois Alcover, Feb 26 2017, after Alois P. Heinz *)

CROSSREFS

Cf. A215977, A051491.

Sequence in context: A215988 A215989 A215980 * A273226 A291726 A280563

Adjacent sequences:  A215976 A215977 A215978 * A215980 A215981 A215982

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 29 2012

STATUS

approved

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Last modified August 18 02:34 EDT 2022. Contains 356204 sequences. (Running on oeis4.)