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A000187 Generalized Euler numbers, c(5,n).
(Formerly M2153 N0858)
2, 30, 3522, 1066590, 604935042, 551609685150, 737740947722562, 1360427147514751710, 3308161927353377294082, 10256718523496425979562270, 39490468691102039103925777602, 184856411587530526077816051412830 (list; graph; refs; listen; history; text; internal format)



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).


Sean A. Irvine, Table of n, a(n) for n = 0..250

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

D. Shanks, Corrigenda to: "Generalized Euler and class numbers", Math. Comp. 22 (1968), 699.

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


From the Shanks paper: Consider the Dirichlet series L_a(s) = sum_{k>=0)} (-a|2k+1) / (2k+1)^s, where (-a|2k+1) is the Jacobi symbol. Then the numbers d_(a,n) are defined by L_a(2n+1)= (Pi/(2a))^(2n+1)*sqrt(a)* c(a,n)/ (2n)! for a>1 and n=0,1,2,... - Sean A. Irvine, Mar 26 2012


a0=5; nmax=20; km0 = nmax; Clear[cc]; L[a_, s_, km_] := Sum[JacobiSymbol[ -a, 2k+1]/(2k+1)^s, {k, 0, km}]; c[a_, n_, km_] := 2^(2n+1)*Pi^(-2n-1)*(2n)!*a^(2n+1/2)*L[a, 2n+1, km] // Round; cc[km_] := cc[km] = Table[ c[a0, n, km], {n, 0, nmax}]; cc[km0]; cc[km = 2km0]; While[cc[km] != cc[ km/2, km = 2km]]; A000187 = cc[km] (* Jean-François Alcover, Feb 05 2016 *)


Cf. A000192, A000490.

Sequence in context: A136636 A220719 A030249 * A053851 A077521 A272445

Adjacent sequences:  A000184 A000185 A000186 * A000188 A000189 A000190




N. J. A. Sloane


More terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jun 02 2000



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Last modified December 12 17:33 EST 2019. Contains 329960 sequences. (Running on oeis4.)