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

0,2

Links

Table of n, a(n) for n=0..29.

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

Prog

(PARI) a(n) = sum(k=0, n\2, (2*k+1)*binomial(2*k, k)*binomial(n-k+1, k+1));

Crossrefs

Cf. A383254, A383503.

Cf. A026569, A377204.

Sequence in context: A166754 A026589 A319792 * A091002 A389293 A330419

Adjacent sequences: A383496 A383497 A383498 * A383500 A383501 A383502

Keyword

nonn

Author

Seiichi Manyama, May 05 2025

Status

approved