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A366012
a(n) = (1/(n+1)) * Sum_{k=0..n} binomial(n+k,k) * binomial(n*(n+1),n-k).
2
1, 2, 13, 156, 2833, 70098, 2214280, 85464984, 3906724321, 206648387550, 12425282899588, 837384222603448, 62539219710804627, 5127758187193514824, 457986530357734020432, 44263628968974498793648, 4602969726808566383149761, 512486177498084438210961270, 60827938291895363867587959628
OFFSET
0,2
FORMULA
a(n) = [x^n] (1/x) * Series_Reversion( x * (1 - x) / (1 + x)^n ).
a(n) ~ exp(n + 3/2) * n^(n - 3/2) / sqrt(2*Pi). - Vaclav Kotesovec, Sep 26 2023
MATHEMATICA
Table[1/(n + 1) Sum[Binomial[n + k, n] Binomial[n (n + 1), n - k], {k, 0, n}], {n, 0, 18}]
Table[SeriesCoefficient[(1/x) InverseSeries[Series[x (1 - x)/(1 + x)^n, {x, 0, n + 1}], x], {x, 0, n}], {n, 0, 18}]
CROSSREFS
Main diagonal of A107111.
Sequence in context: A058192 A367820 A054382 * A297408 A316701 A062593
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Sep 25 2023
STATUS
approved