A369755 Expansion of e.g.f. exp( (1 - (1+x)^4)/4 ).

1, -1, -2, 2, 28, 44, -464, -3088, 1408, 135872, 726976, -2959936, -67261952, -293413888, 3054389248, 52458520064, 178569842176, -3909868400128, -60465254054912, -149165881689088, 6569005278939136, 98054837101881344, 158559568611401728, -14356527387138039808

Offset

0,3

Links

Table of n, a(n) for n=0..23.

Eric Weisstein's World of Mathematics, Bell Polynomial.

Formula

a(0) = 1; a(n) = -(n-1)! * Sum_{k=1..min(4,n)} binomial(3,k-1) * a(n-k)/(n-k)!.

a(n) = Sum_{k=0..n} 4^k * Stirling1(n,k) * Bell_k(-1/4), where Bell_n(x) is n-th Bell polynomial.

D-finite with recurrence a(n) +a(n-1) +3*(n-1)*a(n-2) +3*(n-1)*(n-2)*a(n-3) +(n-1)*(n-2)*(n-3)*a(n-4)=0. - R. J. Mathar, Feb 02 2024

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((1-(1+x)^4)/4)))

Crossrefs

Cf. A001464, A252284, A369756.

Cf. A049426.

Sequence in context: A024577 A121222 A125067 * A193618 A246062 A178955

Adjacent sequences: A369752 A369753 A369754 * A369756 A369757 A369758

Keyword

sign

Author

Seiichi Manyama, Jan 31 2024

Status

approved