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

0, 3, 33, 270, 2025, 14868, 109851, 827508, 6397665, 50932233, 418175274, 3542883864, 30972408558, 279287247333, 2596195945977, 24862074701208, 245091667488207, 2485294443056496, 25903024863885465, 277278282774462210

Offset: 2

Author

N. J. A. Sloane

Keywords

• nonn

References

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

Links

• G. C. Greubel, Table of n, a(n) for n = 2..570
• J. Riordan, The number of impedances of an n-terminal network, Bell Syst. Tech. J., 18 (1939), 300-314.

Crossrefs

Cf. A003128, A003130.

Programs

Magma

[(&+[Binomial(Binomial(k,2),2)*StirlingSecond(n,k): k in [0..n]]): n in [2..40]]; // G. C. Greubel, Nov 04 2022

Mathematica

A003129[n_]:= A003129[n]= Sum[StirlingS2[n,k]*Binomial[Binomial[k,2],2], {k,0,n}];
Table[A003129[n], {n, 0, 40}] (* G. C. Greubel, Nov 04 2022 *)

SageMath

def A003129(n): return sum(binomial(binomial(k,2), 2)*stirling_number2(n,k) for k in range(n+1))
[A003129(n) for n in range(2,40)] # G. C. Greubel, Nov 04 2022

Formula

E.g.f.: (exp(x) + 3)*(exp(x) - 1)^3*exp(exp(x) - 1)/8.

a(n) = Sum_{k=0..n} Stirling2(n,k)*binomial(binomial(k,2),2).