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 A003130 Impedances of an n-terminal network. (Formerly M4873) 3
 1, 12, 157, 1750, 17446, 164108, 1505099, 13720902, 125782441, 1167813944, 11029947952, 106273227216, 1046320856673, 10537366304920, 108606982421301, 1145873284492738, 12375688888657414, 136802023177966948, 1547385154016264531 (list; graph; refs; listen; history; text; internal format)
 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..565 J. Riordan, The number of impedances of an n-terminal network, Bell Syst. Tech. J., 18 (1939), 300-314. FORMULA a(n) = A003128(n) + 2 * A003129(n) + U(n) where U(n) = Sum_{k=2..n} u(n) * Stirling2(n, k), and u(n) = (20(n)_4 + 10(n)_5 + (n)_6) / 8 where (n)_k = n * (n - 1) * ... * (n - k + 1) denotes the falling factorial. - Sean A. Irvine, Feb 03 2015 MATHEMATICA A003128[n_]:= A003128[n]= Sum[StirlingS2[n, k]*Binomial[k, 2], {k, 0, n}]; A003129[n_]:= A003129[n]= Sum[StirlingS2[n, k]*Binomial[Binomial[k, 2], 2], {k, 0, n}]; U[n_]:= Sum[15*k*Binomial[k+1, 5]*StirlingS2[n, k], {k, 0, n}]; A003130[n_]:= A003128[n] +2*A003129[n] +U[n]; Table[A003130[n], {n, 0, 40}] (* G. C. Greubel, Nov 04 2022 *) PROG (Magma) A003128:= func< n | (&+[Binomial(k, 2)*StirlingSecond(n, k): k in [0..n]]) >; A003129:= func< n | (&+[Binomial(Binomial(k, 2), 2)*StirlingSecond(n, k): k in [0..n]]) >; U:= func< n | 15*(&+[k*Binomial(k+1, 5)*StirlingSecond(n, k): k in [0..n]]) >; A003130:= func< n | A003128(n)+ 2*A003129(n) +U(n) >; [A003130(n): n in [2..40]]; // G. C. Greubel, Nov 04 2022 (SageMath) def A003128(n): return sum(binomial(k, 2)*stirling_number2(n, k) for k in range(n+1)) def A003129(n): return sum(binomial(binomial(k, 2), 2)*stirling_number2(n, k) for k in range(n+1)) def U(n): return 15*sum(k*binomial(k+1, 5)*stirling_number2(n, k) for k in range(n+1)) def A003130(n): return A003128(n) +2*A003129(n) +U(n) [A003130(n) for n in range(2, 40)] # G. C. Greubel, Nov 04 2022 CROSSREFS Cf. A003128, A003129. Sequence in context: A110216 A218839 A036276 * A015000 A220225 A213376 Adjacent sequences: A003127 A003128 A003129 * A003131 A003132 A003133 KEYWORD nonn AUTHOR EXTENSIONS More terms from Sean A. Irvine, Feb 03 2015 STATUS approved

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Last modified February 8 11:37 EST 2023. Contains 360138 sequences. (Running on oeis4.)