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
U[n_]:= Sum[15*k*Binomial[k+1, 5]*StirlingS2[n, k], {k, 0, 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(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))
[A003130(n) for n in range(2, 40)] # G. C. Greubel, Nov 04 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Sean A. Irvine, Feb 03 2015
STATUS
approved