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A002735
Related to Euler numbers, expansion of e.g.f. sec(x)*tan^2(x).
(Formerly M3486 N1417)
1
4, 14, 56, 331, 1324, 12284, 49136, 663061, 2652244, 49164554, 196658216, 4798037791, 19192151164, 596372040824, 2385488163296, 91991577140521, 367966308562084, 17244625801225094, 68978503204900376, 3861296322290987251
OFFSET
1,1
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(2*n) = A060075(n). Conjecture a(2*n+1) = 4*a(2*n). - R. J. Mathar, Feb 03 2025
Mathar's conjecture is true: a(2*n+1) = b(2,2*n+1) = 4*b(2,2*n) = 4*a(2*n). - Sela Fried, Dec 08 2025
CROSSREFS
KEYWORD
nonn
EXTENSIONS
More terms from Sean A. Irvine, Sep 25 2015
STATUS
approved