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A003128
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Number of driving-point impedances of an n-terminal network.
(Formerly M4210)
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11
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0, 0, 1, 6, 31, 160, 856, 4802, 28337, 175896, 1146931, 7841108, 56089804, 418952508, 3261082917, 26403700954, 221981169447, 1934688328192, 17454004213180, 162765041827846, 1566915224106221, 15553364227949564, 159004783733999787, 1672432865100333916
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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REFERENCES
| J. Riordan, The number of impedances of an n-terminal network, Bell Syst. Tech. J., 18 (1939), 300-314.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| N. J. A. Sloane, Table of n, a(n) for n = 0..100
R. Suter, Two analogues of a classical sequence, J. Integer Sequences, Vol. 3 (2000), #P00.1.8.
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FORMULA
| a(n) = (Bell(n)-3*Bell(n+1)+Bell(n+2))/2. - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 07 2006
a(n+2) = A123158(n,4) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 06 2006
a(n) = sum {k = 1..n} binomial(k,2)*Stirling2(n,k). a(n) = 1/(2*exp(1))*sum {k>=0} k^n*(k^2-3*k+1)/k!. Note that k^2-3*k+1 = k*(k-1)-2*k+1 is an example of a Poisson-Charlier polynomial. a(n) = D^n(x^2/2!*exp(x)) evaluated at x = 0, where D is the operator (1+x)*d/dx. Cf. A005493. E.g.f.: 1/2*exp(exp(x)-1))*(exp(x)-1)^2 = x^2/2!+6*x^3/3!+31*x^4/4!+.... O.g.f.: sum {k>=0} binomial(k,2)*x^k/product {i=1..k} (1-i*x) = x^2+6*x^3+31*x^4+.... - Peter Bala, Nov 28 2011
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MAPLE
| with(combinat); A000110:=n->sum(stirling2(n, k), k=0..n): f:=n->(A000110(n)-3*A000110(n+1)+A000110(n+2))/2;
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PROG
| (Maxima) makelist((belln(n)-3*belln(n+1)+belln(n+2))/2, n, 0, 12); [Emanuele Munarini, Jul 14 2011]
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CROSSREFS
| Cf. A000110, A003129, A003130, A039759, A039765 etc.
Sequence in context: A038223 A022034 A047665 * A058146 A015449 A162475
Adjacent sequences: A003125 A003126 A003127 * A003129 A003130 A003131
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KEYWORD
| nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 14 2000
Typo in entries corrected by Martin Larsen, Jul 03 2008
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