OFFSET
0,4
COMMENTS
Number of set partitions of [n] whose block lengths are triangular numbers. - Alois P. Heinz, Jun 10 2018
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..603
EXAMPLE
E.g.f.: A(x) = 1 + x + x^2/2! + 2*x^3/3! + 5*x^4/4! + 11*x^5/5! + 32*x^6/6! +...
where
log(A(x)) = x + x^3/3! + x^6/6! + x^10/10! + x^15/15! + x^21/21! +...
MAPLE
a:= proc(n) option remember; `if`(n=0, 1, add(`if`(
issqr(8*j+1), a(n-j)*binomial(n-1, j-1), 0), j=1..n))
end:
seq(a(n), n=0..30); # Alois P. Heinz, Jun 10 2018
MATHEMATICA
m = 30;
CoefficientList[Exp[Sum[x^(n(n+1)/2)/(n(n+1)/2)!, {n, 1, m}]] + O[x]^m, x]* Range[0, m-1]! (* Jean-François Alcover, Mar 05 2021 *)
PROG
(PARI) {a(n)=n!*polcoeff(exp(sum(m=1, sqrtint(2*n+1), x^(m*(m+1)/2)/(m*(m+1)/2)!+x*O(x^n))), n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 31 2012
STATUS
approved