A003129 Number of transfer impedances of an n-terminal network. (Formerly M3131)

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

Offset

2,2

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.

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).

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 *)

Prog

(Magma) [(&+[Binomial(Binomial(k, 2), 2)*StirlingSecond(n, k): k in [0..n]]): n in [2..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

Crossrefs

Cf. A003128, A003130.

Sequence in context: A331193 A206950 A189644 * A190542 A180416 A043038

Adjacent sequences: A003126 A003127 A003128 * A003130 A003131 A003132

Keyword

nonn

Author

N. J. A. Sloane

Status

approved