A367100 a(n) = Sum_{k=0..n} A000108(k) * A000041(k).

1, 2, 6, 21, 91, 385, 1837, 8272, 39732, 185592, 891024, 4183040, 20199964, 95232864, 456282264, 2162574984, 10330196754, 48834699384, 232725598884, 1098684561984, 5214388065324, 24591671545164, 116257200312444, 546797015443194, 2578396047478494, 12098087101521510

Offset

0,2

Links

Table of n, a(n) for n=0..25.

Formula

a(n) ~ 2^(2*n) * exp(Pi*sqrt(2*n/3)) / (3^(3/2) * sqrt(Pi) * n^(5/2)).

Mathematica

Table[Sum[CatalanNumber[k]*PartitionsP[k], {k, 0, n}], {n, 0, 30}]

Crossrefs

Cf. A000041, A000108, A356269, A367101.

Sequence in context: A189243 A033540 A177479 * A147719 A231166 A115089

Adjacent sequences: A367097 A367098 A367099 * A367101 A367102 A367103

Keyword

nonn

Author

Vaclav Kotesovec, Nov 04 2023

Status

approved