The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A003128 Number of driving-point impedances of an n-terminal network. (Formerly M4210) 10
 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; text; internal format)
 OFFSET 0,4 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS N. J. A. Sloane, Table of n, a(n) for n = 0..100 J. Riordan, The number of impedances of an n-terminal network, Bell Syst. Tech. J., 18 (1939), 300-314. R. Suter, Two analogues of a classical sequence, J. Integer Sequences, Vol. 3 (2000), #P00.1.8. FORMULA a(n) = (Bell(n)-3*Bell(n+1)+Bell(n+2))/2. - Vladeta Jovovic, Aug 07 2006 a(n+2) = A123158(n,4). - Philippe Deléham, Oct 06 2006 From Peter Bala, Nov 28 2011: (Start) a(n) = sum {k = 1..n} binomial(k,2)*Stirling2(n,k), Stirling transform of A000217. 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+.... (End) MAPLE with(combinat); A000110:=n->sum(stirling2(n, k), k=0..n): f:=n->(A000110(n)-3*A000110(n+1)+A000110(n+2))/2; MATHEMATICA a[n_] := (BellB[n] - 3*BellB[n+1] + BellB[n+2])/2; Table[a[n], {n, 0, 23}] (* Jean-François Alcover, Jul 12 2012, after Vladeta Jovovic *) max = 23; CoefficientList[ Series[1/2*(E^x - 1)^2*E^(E^x - 1), {x, 0, max}], x]*Range[0, max]! (* Jean-François Alcover, Oct 04 2013, after e.g.f. *) PROG (Maxima) makelist((belln(n)-3*belln(n+1)+belln(n+2))/2, n, 0, 12); [Emanuele Munarini, Jul 14 2011] (Haskell) a003128 n = a003128_list !! n a003128_list = zipWith3 (\x y z -> (x - 3 * y + z) `div` 2)                a000110_list (tail a000110_list) (drop 2 a000110_list) -- Reinhard Zumkeller, Jun 30 2013 (Python) # Python 3.2 or higher required from itertools import accumulate A003128_list, blist, a, b = [], [1], 1, 1 for _ in range(30): ....blist = list(accumulate([b]+blist)) ....c = blist[-1] ....A003128_list.append((c+a-3*b)//2) ....a, b = b, c # Chai Wah Wu, Sep 19 2014 (MAGMA) [(Bell(n) - 3*Bell(n+1) + Bell(n+2))/2: n in [0..30]]; // Vincenzo Librandi, Sep 19 2014 (PARI) a(n)=sum(k=1, n, binomial(k, 2)*stirling(n, k, 2)) \\ Charles R Greathouse IV, Feb 07 2017 CROSSREFS Cf. A000110, A003129, A003130, A039759, A039765. Sequence in context: A022034 A277669 A047665 * A058146 A015449 A162475 Adjacent sequences:  A003125 A003126 A003127 * A003129 A003130 A003131 KEYWORD nonn,nice AUTHOR EXTENSIONS More terms from Vladeta Jovovic, Apr 14 2000 Typo in entries corrected by Martin Larsen, Jul 03 2008 Typo in e.g.f. corrected by Vaclav Kotesovec, Feb 15 2015 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 2 12:56 EDT 2020. Contains 334772 sequences. (Running on oeis4.)