A371836 a(n) = Sum_{k=0..floor(n/2)} n^k * binomial(2*n-2*k-1,n-2*k).
1, 1, 5, 19, 91, 426, 2190, 11467, 63811, 365806, 2200978, 13677962, 88553726, 591576220, 4093814812, 29164567635, 214244414371, 1616044475734, 12523774634922, 99418836782602, 808492937082410, 6720935024074092, 57100849909374340, 495022008799053006
Offset: 0
Keywords
Programs
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Mathematica
Join[{1}, Table[Sum[n^k*Binomial[2*n-2*k-1,n-1], {k, 0, n/2}], {n, 1, 25}]] (* Vaclav Kotesovec, Apr 08 2024 *) -
PARI
a(n) = sum(k=0, n\2, n^k*binomial(2*n-2*k-1, n-2*k));
Formula
a(n) = [x^n] 1/((1-n*x^2) * (1-x)^n).
a(n) ~ exp(sqrt(n) + 1/2) * n^(n/2) / 2. - Vaclav Kotesovec, Apr 08 2024