A002435 Second-order Euler numbers. (Formerly M1686 N0665)

0, 2, 6, 28, 180, 662, 7266, 24568, 408360, 1326122, 30974526, 98329108, 3065784540, 9596075582, 384653685786, 1192744081648, 59724464976720, 183983154281042, 11249503075325046, 34489251602450188, 2527964965265232900, 7722592644581974502, 668249973079223076306

Offset

1,2

References

A. Fletcher, J. C. P. Miller, L. Rosenhead and L. J. Comrie, An Index of Mathematical Tables. Vols. 1 and 2, 2nd ed., Blackwell, Oxford and Addison-Wesley, Reading, MA, 1962, Vol. 1, p. 75.

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

Seiichi Manyama, Table of n, a(n) for n = 1..482

M. A. Stern, Zur Theorie der Eulerschen Zahlen, J. Reine Angew. Math., 79 (1875), 67-98.

Index entries for sequences related to Stern's sequences

Formula

a(n) = A104035(n,2) for even n, and a(n) = A104035(n,3) for odd n. - Seiichi Manyama, Apr 29 2026

Maple

F := 2/(exp(x)+exp(-x)): z := ((exp(x)-exp(-x))/(exp(x)+exp(-x)))^2: w := simplify(diff(z, x)): p := proc(n) if n mod 2 = 0 then simplify(subs(x=0, (-1)^(1+floor(n/2))*simplify(diff(diff(F, x$n)/F, x)/w))) else simplify(subs(x=0, (-1)^(1+floor(n/2))*simplify(diff(diff(F, x$n)/simplify(diff(F, x)), x)/w))) fi end: seq(p(n), n=1..28); # Emeric Deutsch, Mar 09 2004

Crossrefs

Cf. A008294, A104035.

Sequence in context: A140092 A052809 A136631 * A276911 A104018 A100526

Adjacent sequences: A002432 A002433 A002434 * A002436 A002437 A002438

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Emeric Deutsch, Mar 09 2004

Status

approved