A383499 Expansion of 1/sqrt( (1-x) * (1-x-4*x^2)^3 ).
1, 2, 9, 22, 71, 186, 537, 1434, 3957, 10586, 28603, 76266, 203767, 540986, 1435533, 3796050, 10026015, 26422350, 69544765, 182759750, 479731113, 1257750486, 3294264627, 8619879726, 22535782953, 58869786162, 153671378139, 400861115498, 1045005290059, 2722601576322
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n\2, (2*k+1)*binomial(2*k, k)*binomial(n-k+1, k+1));
Formula
a(n) = Sum_{k=0..floor(n/2)} (2*k+1) * binomial(2*k,k) * binomial(n-k+1,k+1).
a(n) ~ sqrt(n/Pi) * ((1 + sqrt(17))/2)^(n + 5/2) / 17^(3/4). - Vaclav Kotesovec, May 05 2025