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A257675 a(n) = A257673(2n,n). 3
1, 3, 21, 174, 1509, 13473, 122580, 1129999, 10518477, 98644395, 930607321, 8821717743, 83960385396, 801783097911, 7678690148647, 73721697254874, 709323064431597, 6837868454315828, 66028546945097793, 638555320797561440, 6183787002091288969, 59957399899953193063 (list; graph; refs; listen; history; text; internal format)
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);

CROSSREFS

Cf. A000219, A257673.

Sequence in context: A247480 A228923 A287995 * A195105 A285272 A295541

Adjacent sequences:  A257672 A257673 A257674 * A257676 A257677 A257678

KEYWORD

nonn

AUTHOR

Alois P. Heinz, May 03 2015

STATUS

approved

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Last modified July 29 07:00 EDT 2021. Contains 346340 sequences. (Running on oeis4.)