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A032186 Shifts left 2 places under "CIJ" (necklace, indistinct, labeled) transform. 1
1, 1, 1, 2, 6, 27, 160, 1183, 10477, 108149, 1275024, 16903440, 248915119, 4031045212, 71202358081, 1362297883463, 28066342411395, 619474462826562, 14583353438928682, 364748466791800669, 9658964416375216576, 269978766441123241685, 7943074999430019396711 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..426

FORMULA

E.g.f. A(x) satisfies differential equation A''(x)=log(1/(1-A(x)), A'(0)=1, A''(0)=1. - Vladimir Kruchinin, Nov 18 2011

a(n) = n!*b(n), b(n) = b(n-2)*(n-2) + sum(i=0..n-4, b(i+3)*(i+1)*(i+2)*(i+3)*b(n-3-i)))/(n*(n-1)*(n-2)) n > 0, b(1)=1, b(2)=1/2. - Vladimir Kruchinin, Nov 18 2011

PROG

(Maxima)

a(n):=if n<3 then 1/n! else (a(n-2)*(n-2)+sum(a(i+3)*(i+1)*(i+2)*(i+3)*a(n-3-i), i, 0, n-4))/(n*(n-1)*(n-2));

makelist(n!*a(n), n, 1, 17); /* Vladimir Kruchinin, Nov 18 2011 */

(PARI)

CIJ(p)={-log(1-p)}

seq(n)={my(p=x+O(x*x^(n%2))); for(i=1, n\2, p=intformal(1 + intformal(1 + CIJ(p)))); Vec(serlaplace(p))} \\ Andrew Howroyd, Sep 19 2018

CROSSREFS

Sequence in context: A118192 A058133 A009308 * A122938 A234568 A231934

Adjacent sequences:  A032183 A032184 A032185 * A032187 A032188 A032189

KEYWORD

nonn,eigen

AUTHOR

Christian G. Bower

STATUS

approved

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Last modified October 23 02:28 EDT 2018. Contains 316518 sequences. (Running on oeis4.)