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A001941 Absolute values of coefficients of an elliptic function.
(Formerly M4411 N1864)
6
1, 7, 35, 140, 483, 1498, 4277, 11425, 28889, 69734, 161735, 362271, 786877, 1662927, 3428770, 6913760, 13660346, 26492361, 50504755, 94766875, 175221109, 319564227, 575387295, 1023624280, 1800577849, 3133695747, 5399228149, 9214458260, 15584195428 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

A. Cayley, A memoir on the transformation of elliptic functions, Collected Mathematical Papers. Vols. 1-13, Cambridge Univ. Press, London, 1889-1897, Vol. 9, p. 128.

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

T. D. Noe, Table of n, a(n) for n = 0..1000

A. Cayley, A memoir on the transformation of elliptic functions, Philosophical Transactions of the Royal Society of London (1874): 397-456; Collected Mathematical Papers. Vols. 1-13, Cambridge Univ. Press, London, 1889-1897, included in Vol. 9. [Annotated scan of pages 126-129]

FORMULA

G.f.: Product ( 1 - x^k )^-c(k), c(k) = 7, 7, 7, 0, 7, 7, 7, 0, ....

a(n) ~ 7^(1/4) * exp(sqrt(7*n/2)*Pi) / (256*2^(3/4)*n^(3/4)). - Vaclav Kotesovec, Nov 15 2017

G.f.: Product_{k>=1} ((1 + x^(2*k))/(1 - x^(2*k-1)))^7. - Ilya Gutkovskiy, Dec 04 2017

MATHEMATICA

nn = 4*10; b = Flatten[Table[{7, 7, 7, 0}, {nn/4}]]; CoefficientList[x*Series[Product[1/(1 - x^m)^b[[m]], {m, nn}], {x, 0, nn}], x] (* T. D. Noe, Aug 17 2012 *)

nmax = 40; CoefficientList[Series[Product[((1 - x^(4*k)) / (1 - x^k))^7, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 15 2017 *)

CROSSREFS

Cf. A001935, A001936, A001937, A001939, A001940, A092877, A093160.

Sequence in context: A124090 A250284 A059595 * A320050 A160460 A160539

Adjacent sequences:  A001938 A001939 A001940 * A001942 A001943 A001944

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Simon Plouffe

STATUS

approved

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Last modified January 18 16:40 EST 2019. Contains 319271 sequences. (Running on oeis4.)