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A235605 Shanks's array c_{a,n} (a >= 1, n >= 0) that generalizes Euler and class numbers, read by antidiagonals upwards. 5
1, 1, 1, 1, 3, 5, 1, 8, 57, 61, 2, 16, 352, 2763, 1385, 2, 30, 1280, 38528, 250737, 50521, 1, 46, 3522, 249856, 7869952, 36581523, 2702765, 2, 64, 7970, 1066590, 90767360, 2583554048, 7828053417, 199360981, 2, 96, 15872, 3487246, 604935042, 52975108096 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Lars Blomberg, Table of n, a(n) for n = 0..5049

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

D. Shanks, Corrigendum: 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]

FORMULA

Shanks gives recurrences.

EXAMPLE

The array begins:

A000364: 1, 1,    5,     61,       1385,         50521,          2702765,..

A000281: 1, 3,   57,   2763,     250737,      36581523,       7828053417,..

A000436: 1, 8,  352,  38528,    7869952,    2583554048,    1243925143552,..

A000490: 1,16, 1280, 249856,   90767360,   52975108096,   45344872202240,..

A000187: 2,30, 3522,1066590,  604935042,  551609685150,  737740947722562,..

A000192: 2,46, 7970,3487246, 2849229890, 3741386059246, 7205584123783010,..

A064068: 1,64,15872,9493504,10562158592,18878667833344,49488442978598912,..

...

MATHEMATICA

amax = 10; nmax = amax-1; km0 = 10; Clear[cc]; L[a_, s_, km_] := Sum[ JacobiSymbol[-a, 2k+1]/(2k+1)^s, {k, 0, km}]; c[1, n_, km_] := 2(2n)! L[1, 2n+1, km] (2/Pi)^(2n+1) // Round; c[a_ /; a>1, n_, km_] := (2n)! L[a, 2n+1, km] (2a/Pi)^(2n+1)/Sqrt[a] // Round; cc[km_] := cc[km] = Table[ c[a, n, km], {a, 1, amax}, {n, 0, nmax}]; cc[km0]; cc[km = 2km0]; While[ cc[km] != cc[km/2, km = 2km]]; A235605[a_, n_] := cc[km][[a, n+1 ]]; Table[ A235605[ a-n, n], {a, 1, amax}, {n, 0, a-1}] // Flatten (* Jean-Fran├žois Alcover, Feb 05 2016 *)

CROSSREFS

Rows: A000364 (Euler numbers), A000281, A000436, A000490, A000187, A000192, A064068, A064069, A064070, A064071, ...

Columns: A000003 (class numbers), A000233, A000362, A000508, ...

Cf. A235606.

Sequence in context: A236631 A302800 A197326 * A212695 A209422 A320386

Adjacent sequences:  A235602 A235603 A235604 * A235606 A235607 A235608

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Jan 22 2014

EXTENSIONS

a(27) removed, a(29)-a(42) added, and typo in name corrected by Lars Blomberg, Sep 10 2015

STATUS

approved

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Last modified August 18 13:12 EDT 2019. Contains 326100 sequences. (Running on oeis4.)