A381276 - OEIS

%I #12 Feb 19 2025 03:37:08

%S 1,1,1,-26,-107,136,9181,53488,-427895,-10486016,-43859879,1373548672,

%T 23512856797,-30564574208,-6412871847563,-73709639926784,

%U 1060067525174929,40587133606543360,179320588932698929,-14474677657838059520,-306563699887974043739,2301792469199499132928

%N Expansion of e.g.f. exp(x * cos(3*x)).

%C As stated in the comment of A185951, A185951(n,0) = 0^n.

%F a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} (-9)^k * (2*k+1) * binomial(n-1,2*k) * a(n-2*k-1).

%F a(n) = Sum_{k=0..n} (3*i)^(n-k) * A185951(n,k), where i is the imaginary unit.

%o (PARI) a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));

%o a(n) = sum(k=0, n, (3*I)^(n-k)*a185951(n, k));

%Y Cf. A009189, A381275.

%Y Cf. A185951, A352643, A381283.

%K sign,new

%O 0,4

%A _Seiichi Manyama_, Feb 18 2025