login
A325948
a(n) = 4^n * [x^n] sqrt(1-x) * Product_{k>=1} 1/(1 - x^k).
2
1, 2, 22, 116, 806, 4028, 26876, 132776, 808710, 4170604, 23586836, 120316888, 673359196, 3383189976, 18228019512, 92654842960, 486382544838, 2443171359820, 12694346947492, 63262412763896, 323739858349684, 1609270321201800, 8117702067063368, 40102791350319408
OFFSET
0,2
FORMULA
a(n) ~ sqrt(Pi) * exp(Pi*sqrt(2*n/3)) * 2^(2*n - 9/4) / (3^(3/4) * n^(5/4)).
a(n) = A325947(n) - 4*A325947(n-1).
MATHEMATICA
nmax = 30; CoefficientList[Series[(1-x)^(1/2) * Product[1/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x] * 4^Range[0, nmax]
Table[4^n*(PartitionsP[n] - Sum[PartitionsP[n-k] * CatalanNumber[k-1]/2^(2*k - 1), {k, 1, n}]), {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, May 28 2019
STATUS
approved