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Search: id:A000436
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| A000436 |
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Generalized Euler numbers.
(Formerly M4584 N1955)
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+0
9
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| 1, 8, 352, 38528, 7869952, 2583554048, 1243925143552, 825787662368768, 722906928498737152, 806875574817679474688, 1118389087843083461066752, 1884680130335630169428983808, 3794717805092151129643367268352
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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D. Shanks, Generalized Euler and class numbers, Math. Comp. 21 (1967), 689-694; 22 (1968), 699.
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).
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LINKS
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Michael E. Hoffman, DERIVATIVE POLYNOMIALS, EULER POLYNOMIALS, AND ASSOCIATED INTEGER SEQUENCES (see Th. 3.3)
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FORMULA
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E.g.f.: cos x / cos 3x.
For n>0, a(n) = A002114(n)*2^(2n+1) = (1/3)*A002112(n)*2^(2n+1) . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Jan 17 2004
a(n)=Sum_{k, 0<=k<=n}(-1)^k*9^(n-k)*A086646(n,k) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 27 2006
(-1)^n a(n)=1-sum_{i=0,1,...,n-1) (-1)^i*binomial(2n,2i)*3^(2n-2i)*a(i). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 19 2006
P_{2n}(sqrt(3))/sqrt(3) (where the polynomials P_n() are defined in A155100). [njas, Nov 05 2009]
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MAPLE
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A000436 := proc(nmax) local a, n, an; a := [1] : n := 1 : while nops(a)< nmax do an := 1-sum(binomial(2*n, 2*i)*3^(2*n-2*i)*(-1)^i*op(i+1, a), i=0..n-1) : a := [op(a), an*(-1)^n] ; n := n+1 ; od ; RETURN(a) ; end: A000436(10) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 19 2006
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CROSSREFS
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Bisections: A156177 and A156178.
Sequence in context: A046244 A079485 A158363 this_sequence A015507 A167256 A038016
Adjacent sequences: A000433 A000434 A000435 this_sequence A000437 A000438 A000439
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KEYWORD
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nonn,new
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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