A111601 Exponential (binomial) convolution of A001818 (with interspersed zeros) and A000142 (factorials).

1, 2, 9, 36, 225, 1350, 11025, 88200, 893025, 8930250, 108056025, 1296672300, 18261468225, 255660555150, 4108830350625, 65741285610000, 1187451971330625, 21374135483951250, 428670161650355625, 8573403233007112500

Offset

1,2

Links

Table of n, a(n) for n=1..20.

Formula

E.g.f.: (1/sqrt(1-x^2))*x/(1-x).

a(n) = n!*Sum_{k=0..floor((n-1)/2)} binomial(2*k, k)/(4^k).

a(2*k+1) = A111595(2*k+2, 0)= ((2*k+1)!!)^2 = A001818(k+1), k >= 0.

D-finite with recurrence (-n+1)*a(n) +n*a(n-1) +n*(n-1)^2*a(n-2)=0. a(1)=1, a(2)=2. - Sergei N. Gladkovskii, Jul 27 2012, corrected Aug 11 2025

a(n) ~ 2*n^(n+1)/exp(n). - Vaclav Kotesovec, Apr 29 2026

Crossrefs

Second column (m=1) of triangle |A111595|.

Sequence in context: A003161 A305206 A101610 * A328268 A330346 A280351

Adjacent sequences: A111598 A111599 A111600 * A111602 A111603 A111604

Keyword

nonn,easy

Author

Wolfdieter Lang, Aug 23 2005

Status

approved