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A007558 Shifts 2 places left when e.g.f. is squared.
(Formerly M1230)
9
1, 1, 1, 2, 4, 10, 30, 100, 380, 1600, 7400, 37400, 204600, 1205600, 7612000, 51260000, 366784000, 2778820000, 22222332000, 187067320000, 1653461480000, 15310662400000, 148217381840000, 1497226615280000, 15754506226800000, 172407188412800000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

REFERENCES

O Bodini, M Dien, X Fontaine, A Genitrini, H K Hwang, Increasing Diamonds, in LATIN 2016: 12th Latin American Symposium, Ensenada, Mexico, April 11-15, 2016, Proceedings Pages pp 207-219 2016 DOI 10.1007/978-3-662-49529-2_16 Lecture Notes in Computer Science Series Volume 9644

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Alois P. Heinz and Vaclav Kotesovec, Table of n, a(n) for n = 0..518 (first 200 terms from Alois P. Heinz)

M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, arXiv:math/0205301 [math.CO], 2002; Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]

M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]

FORMULA

a(n) ~ c * d^n * n! * n, where d = 0.42089835222875301896706732846764190595145230471243866202153775712470703269... is the root of the equation WeierstrassP(1/d, 0, -1/108) = 1/6 and c = 1.06293253745327664869312823202016275205862332741406172188742740834633... - Vaclav Kotesovec, Sep 06 2014, updated Nov 27 2020

E.g.f.: 6^(1/3) * WeierstrassP((x+c)/6^(1/3), 0, -1/3), where c = 9.1898572290187191497581591181140131456801040793456712149069964791654... is the root of the equation WeierstrassP(c/6^(1/3), 0, -1/3) = 6^(-1/3). - Vaclav Kotesovec, Jun 14 2015

E.g.f. A(x) satisfies: A(x) = 1 + x + Integral(Integral A(x)^2 dx) dx. - Ilya Gutkovskiy, Jul 04 2020

MAPLE

a:= proc(n) option remember;

`if`(n<2, 1, add(a(i)*a(n-2-i) *binomial(n-2, i), i=0..n-2))

end:

seq(a(n), n=0..30); # Alois P. Heinz, Jun 22 2012

MATHEMATICA

a[n_] := a[n] = If[n < 2, 1, Sum[a[i] * a[n - 2 - i] * Binomial[n - 2, i], {i, 0, n - 2}]]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Feb 03 2014, after Alois P. Heinz *)

Table[SeriesCoefficient[1 + (18 (WeierstrassP[x, {0, -1/108}] - WeierstrassPPrime[x, {0, -1/108}]))/(6 WeierstrassP[x, {0, -1/108}] - 1)^2, {x, 0, k}] k!, {k, 0, 30}] (* Jan Mangaldan, Nov 27 2020 *)

CROSSREFS

Sequence in context: A087161 A337488 A328358 * A094957 A000733 A092073

Adjacent sequences: A007555 A007556 A007557 * A007559 A007560 A007561

KEYWORD

nonn,nice,eigen

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified January 29 15:13 EST 2023. Contains 359923 sequences. (Running on oeis4.)