cp's OEIS Frontend

A003129 Number of transfer impedances of an n-terminal network.

%I A003129 M3131 #19 Nov 04 2022 13:37:28
%S A003129 0,3,33,270,2025,14868,109851,827508,6397665,50932233,418175274,
%T A003129 3542883864,30972408558,279287247333,2596195945977,24862074701208,
%U A003129 245091667488207,2485294443056496,25903024863885465,277278282774462210
%N A003129 Number of transfer impedances of an n-terminal network.
%D A003129 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A003129 G. C. Greubel, <a href="/A003129/b003129.txt">Table of n, a(n) for n = 2..570</a>
%H A003129 J. Riordan, <a href="https://archive.org/details/bstj18-2-300">The number of impedances of an n-terminal network</a>, Bell Syst. Tech. J., 18 (1939), 300-314.
%F A003129 E.g.f.: (exp(x) + 3)*(exp(x) - 1)^3*exp(exp(x) - 1)/8.
%F A003129 a(n) = Sum_{k=0..n} Stirling2(n,k)*binomial(binomial(k,2),2).
%t A003129 A003129[n_]:= A003129[n]= Sum[StirlingS2[n,k]*Binomial[Binomial[k,2],2], {k,0,n}];
%t A003129 Table[A003129[n], {n, 0, 40}] (* _G. C. Greubel_, Nov 04 2022 *)
%o A003129 (Magma) [(&+[Binomial(Binomial(k,2),2)*StirlingSecond(n,k): k in [0..n]]): n in [2..40]]; // _G. C. Greubel_, Nov 04 2022
%o A003129 (SageMath)
%o A003129 def A003129(n): return sum(binomial(binomial(k,2), 2)*stirling_number2(n,k) for k in range(n+1))
%o A003129 [A003129(n) for n in range(2,40)] # _G. C. Greubel_, Nov 04 2022
%Y A003129 Cf. A003128, A003130.
%K A003129 nonn
%O A003129 2,2
%A A003129 _N. J. A. Sloane_