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A235606 Shanks's array d_{a,n} (a >= 1, n >= 1) that generalizes the tangent numbers, read by antidiagonals upwards. 4
1, 1, 2, 2, 11, 16, 4, 46, 361, 272, 4, 128, 3362, 24611, 7936, 6, 272, 16384, 515086, 2873041, 353792, 8, 522, 55744, 4456448, 135274562, 512343611, 22368256, 8, 904, 152166, 23750912, 2080374784, 54276473326, 129570724921, 1903757312, 12, 1408, 355688 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

REFERENCES

D. Shanks. "Generalized Euler and Class Numbers." Math. Comput. 21, 689-694, 1967. Math. Comput. 22, 699, 1968.

LINKS

Lars Blomberg, Table of n, a(n) for n = 1..5050

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

FORMULA

Shanks gives recurrences.

EXAMPLE

The array begins:

A000182: 1,  2,    16,      272,        7936,         353792, ...

A000464: 1, 11,   361,    24611,     2873041,      512343611, ...

A000191: 2, 46,  3362,   515086,   135274562,    54276473326, ...

A000318: 4,128, 16384,  4456448,  2080374784,  1483911200768, ...

A000320: 4,272, 55744, 23750912, 17328937984, 19313964388352, ...

A000411: 6,522,152166, 93241002, 97949265606,157201459863882, ...

A064072: 8,904,355688,296327464,423645846728,925434038426824, ...

...

MATHEMATICA

amax = nmax = 10; km0 = 10; Clear[dd]; L[a_, s_, km_] := Sum[JacobiSymbol[ -a, 2k+1]/(2k+1)^s, {k, 0, km}]; d[1, n_, km_] := 2(2n-1)! L[-1, 2n, km] (2/Pi)^(2n) // Round; d[a_ /; a>1, n_, km_] := (2n-1)! L[-a, 2n, km] (2a/ Pi)^(2n)/Sqrt[a] // Round; dd[km_] := dd[km] = Table[d[a, n, km], {a, 1, amax}, {n, 1, nmax}]; dd[km0]; dd[km = 2km0]; While[dd[km] != dd[km/2, km = 2km]]; A235606 = dd[km]; Table[A235606[[ a-n+1, n]], {a, 1, amax}, {n, 1, a}] // Flatten (* Jean-François Alcover, Feb 05 2016 *)

CROSSREFS

Rows: A000182 (tangent numbers), A000464, A000191, A000318, A000320, A000411, A064072-A064075, ...

Columns: A000061, A000176, A000488, A000518, ...

Cf. A235605.

Sequence in context: A279197 A121871 A194638 * A175202 A187430 A151365

Adjacent sequences:  A235603 A235604 A235605 * A235607 A235608 A235609

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Jan 22 2014

EXTENSIONS

More terms from Lars Blomberg, Sep 07 2015

STATUS

approved

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Last modified August 26 00:35 EDT 2019. Contains 326324 sequences. (Running on oeis4.)