A390032 - OEIS

A390032

Number of perfect overpartitions of 2*n-1: A390030(2*n-1).

2, 5, 5, 13, 5, 19, 5, 34, 13, 19, 5, 65, 5, 19, 21, 89, 5, 61, 5, 65, 21, 19, 5, 210, 13, 19, 32, 65, 5, 103, 5, 233, 21, 19, 21, 248, 5, 19, 21, 210, 5, 103, 5, 65, 70, 19, 5, 654, 13, 61, 21, 65, 5, 177, 21, 210, 21, 19, 5, 431, 5, 19, 70, 610, 21, 103, 5, 65, 21, 103

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..70.

FORMULA

a(n) = A390030(2*n-1).

a(n) = Sum_{r=0..s} Sum_{v=r..s} binomial(v,r)*f_v(2*n), where s = A007814(2*n) and f_v(N) is the number of ordered factorizations of N having v copies of 2.

EXAMPLE

For n=2, the a(3)=5 perfect overpartitions of 3 are (1,1,1), (2,1), (2',1), (2,1'), (2',1').

CROSSREFS

Cf. A390030, A390031, A352063.

Sequence in context: A183719 A379564 A239340 * A124201 A100953 A112835

Adjacent sequences: A390029 A390030 A390031 * A390033 A390034 A390035

KEYWORD

nonn

AUTHOR

Augustine O. Munagi, Oct 28 2025

STATUS

approved