A002735 Related to Euler numbers, expansion of e.g.f. sec(x)*tan^2(x).
4, 14, 56, 331, 1324, 12284, 49136, 663061, 2652244, 49164554, 196658216, 4798037791, 19192151164, 596372040824, 2385488163296, 91991577140521, 367966308562084, 17244625801225094, 68978503204900376, 3861296322290987251
Offset: 1
Keywords
References
- N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Links
- C. Krishnamachary and M. Bheemasena Rao, Determinants whose elements are Eulerian, prepared Bernoullian and other numbers, J. Indian Math. Soc., 14 (1922), 55-62, 122-138 and 143-146. See p. 146. [Annotated scanned copy]
Formula
a(n) = b(2,n) where b(m,1) = m^2, b(m,2*n) = Sum_{k=1..m+1} b(k,2*n-1), b(m,2*n+1) = m^2 * b(m, 2*n). Note, A000364(n) = b(1, 2*n). - Sean A. Irvine, Sep 25 2015
a(2n) = A060075(n). Conjecture a(2n+1)=4*a(2n). - R. J. Mathar, Feb 03 2025
Extensions
More terms from Sean A. Irvine, Sep 25 2015