0,3

Let B_n(x) = Sum_{k=0.. n*(n-1)/2} b(n,k)*x^k, where b(n,k) is number of n-node acyclic digraphs with k arcs, cf. A081064; then a(n) = |B_n(-2)|. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Jan 25 2005

V. I. Arnold, Springer numbers and Morsification spaces. J. Algebraic Geom. 1 (1992), no. 2, 197-214.

V. I. Arnold, The calculus of snakes and the combinatorics of Bernoulli, Euler and Springer numbers of Coxeter groups, Uspekhi Mat. nauk., 47 (#1, 1992), 3-45 = Russian Math. Surveys, Vol. 47 (1992), 1-51.

D. Dumont, Further triangles of Seidel-Arnold type and continued fractions related to Euler and Springer numbers, Adv. Appl. Math., 16 (1995), 275-296.

D. Shanks, Generalized Euler and class numbers, Math. Comp. 21 (1967), 689-694; 22 (1968), 699.

Zhi-Hong Sun, Congruences involving Bernoulli polynomials, Discr. Math., 308 (2007), 71-112.

T. D. Noe, Table of n, a(n) for n=0..100

E.g.f.: 1/(cos x - sin x).

G.f. A(x)=y satisfies y'^2=2y^4-y^2, y''y=y^2+2y'^2. - Michael Somos Feb 03 2004

(PARI) a(n)=if(n<0, 0, n!*polcoeff(1/(cos(x+x*O(x^n))-sin(x+x*O(x^n))), n)) (from Michael Somos)

(PARI) {a(n)=local(an); if(n<2, n>=0, an=vector(n+1, m, 1); for(m=2, n, an[m+1]=2*an[m]+an[m-1]+sum(k=0, m-3, binomial(m-2, k)*( an[k+1]*an[m-1-k]+2*an[k+2]*an[m-k]-an[k+3]*an[m-1-k] ))); an[n+1])} (from Michael Somos)

Cf. A007836.

Bisections are A000281 and A000464.

Related polynomials are given in A098432.

Cf. A079858.

Adjacent sequences: A001583 A001584 A001585 this_sequence A001587 A001588 A001589

Sequence in context: A000985 A094611 A052442 this_sequence A126201 A020012 A126100

nonn,easy,nice

njas

More terms from Vladeta Jovovic (vladeta(AT)Eunet.yu), Jan 25 2005