A382958 a(n) = (n!)^2 * [(x*y)^n] Product_{k>=1} 1 / (1 - (x^k + y^k)/k!).
1, 2, 30, 920, 53078, 4828892, 643086588, 117718532696, 28378716172822, 8713799596723484, 3320414836230009080, 1537509304647364575716, 850310874146059999520372, 553587598414859641796343780, 419087377790397643526857611312, 365040505934072220586791778761920
Offset: 0
Keywords
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 0..100
Programs
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Mathematica
Table[(n!)^2 SeriesCoefficient[Product[1/(1 - (x^k + y^k)/k!), {k, 1, n}], {x, 0, n}, {y, 0, n}], {n, 0, 15}]
Formula
a(n) ~ c * sqrt(Pi) * 2^(2*n + 1) * n^(2*n + 1/2) / exp(2*n), where c = Product_{k>=2} (1 + 1/(2^(k-1)*k! - 1)) = 1.399382837233736726730568376611759424994992988... - Vaclav Kotesovec, Apr 24 2025