A032187 Shifts left 3 places under "CIJ" (necklace, indistinct, labeled) transform.

1, 1, 1, 1, 2, 6, 26, 151, 1093, 9489, 96084, 1111722, 14469388, 209234595, 3328056991, 57746229265, 1085448899206, 21972175778646, 476535125344462, 11024061833485335, 270965694793159153, 7051933526740491393, 193723061625591928384, 5601822117610355927946

Offset

1,5

Links

Andrew Howroyd, Table of n, a(n) for n = 1..200

Formula

a(n) = sum(k=0..n-5, binomial(n-4,k)*a(k+4)*a(n-k-4)) + a(n-3), n>4, a(1)=a(2)=a(3)=a(4)=1. - Vladimir Kruchinin, May 10 2011

E.g.f. A(x) satisfies differential equation A'''(x)=log(1/(1-A(x))), A'(0)=1, A''(0)=1, A'''(0)=1. - Vladimir Kruchinin, Nov 19 2011

Prog

(Maxima)
a(n):=if n=0 then 0 else if n<5 then 1 else sum(binomial(n-4, k)*a(k+4)*a(n-k-4), k, 0, n-5)+a(n-3); /* Vladimir Kruchinin, May 10 2011 */
(PARI)
CIJ(p)={-log(1-p)}
seq(n)={my(p=x+x^2+O(x*x^(n%3))); for(i=1, n\3, p=intformal(1 + intformal(1 + intformal(1 + CIJ(p))))); Vec(serlaplace(p))} \\ Andrew Howroyd, Sep 19 2018

Crossrefs

Sequence in context: A159311 A000629 A185994 * A372236 A003659 A159602

Adjacent sequences: A032184 A032185 A032186 * A032188 A032189 A032190

Keyword

nonn,eigen

Author

Christian G. Bower

Extensions

Terms a(22) and beyond from Andrew Howroyd, Sep 19 2018

Status

approved