A373770 Expansion of e.g.f. exp(x^2 / (2 * (1 - x))) / (1 - x).

1, 1, 3, 12, 63, 405, 3075, 26880, 265545, 2922885, 35447895, 469396620, 6736095135, 104102463465, 1723322736135, 30416726340000, 570089983287825, 11306156398562025, 236514323713142475, 5204122351983254700, 120139520273298100575, 2903216115946088267325

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = n! * Sum_{k=0..floor(n/2)} binomial(n-k,n-2*k)/(2^k * k!).

From Vaclav Kotesovec, Jun 18 2024: (Start)

Recurrence: 2*a(n) = 2*(2*n-1)*a(n-1) - 2*(n-2)*(n-1)*a(n-2) - (n-2)*(n-1)*a(n-3).

a(n) ~ 2^(-1/4) * exp(-3/4 + sqrt(2*n) - n) * n^(n + 1/4) * (1 + 7/(6*sqrt(2*n))). (End)

Prog

(PARI) a(n) = n!*sum(k=0, n\2, binomial(n-k, n-2*k)/(2^k*k!));

Crossrefs

Cf. A130905, A361596, A373771.

Cf. A185369.

Sequence in context: A264151 A186186 A355164 * A238887 A375394 A351778

Adjacent sequences: A373767 A373768 A373769 * A373771 A373772 A373773

Keyword

nonn

Author

Seiichi Manyama, Jun 18 2024

Status

approved