A257675 a(n) = A257673(2n,n).

1, 3, 21, 174, 1509, 13473, 122580, 1129999, 10518477, 98644395, 930607321, 8821717743, 83960385396, 801783097911, 7678690148647, 73721697254874, 709323064431597, 6837868454315828, 66028546945097793, 638555320797561440, 6183787002091288969, 59957399899953193063

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..500

Formula

a(n) = A257673(2n,n).

a(n) ~ c * d^n / sqrt(n), where d = 9.93288639318036180192949205242384178223421389697248991016311001938239..., c = 0.31807008223273549425589833682845775837952038959... . - Vaclav Kotesovec, May 19 2015

a(n) = [x^(2*n)] (-1 + Product_{k>=1} 1 / (1 - x^k)^k)^n. - Ilya Gutkovskiy, Feb 13 2021

Maple

g:= proc(n) option remember; `if`(n=0, 1, add(
      g(n-j)*numtheory[sigma][2](j), j=1..n)/n)
    end:
b:= proc(n, k) option remember; `if`(k<2, g(n+1), (q->
      add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2)))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..22);

Mathematica

g[n_] := g[n] = If[n == 0, 1, Sum[g[n - j]*
     DivisorSigma[2, j], {j, 1, n}]/n];
b[n_, k_] := b[n, k] = If[k < 2, g[n+1], With[{q = Quotient[k, 2]},
     Sum[b[j, q] b[n - j, k - q], {j, 0, n}]]];
a[n_] := b[n, n];
Table[a[n], {n, 0, 22}] (* Jean-François Alcover, Aug 23 2021, after Alois P. Heinz *)

Crossrefs

Cf. A000219, A257673.

Sequence in context: A228923 A287995 A379086 * A372108 A195105 A285272

Adjacent sequences: A257672 A257673 A257674 * A257676 A257677 A257678

Keyword

nonn

Author

Alois P. Heinz, May 03 2015

Status

approved