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A272630
a(n) = binomial(3*prime(n), prime(n)) - 3*binomial(2*prime(n), prime(n)) + 3.
1
0, 27, 2250, 105987, 191420427, 8091223647, 14764068268068, 636877933530303, 1202912275541006163, 101416777765228668135243, 4470228055779262703971971, 387215990724249198145972139532, 763815804413169191825705670410076, 33986135421741862065520464883016403
OFFSET
1,2
LINKS
Chun-Gang Ji, A simple proof of a curious congruence by Zhao, Proc. Amer. Math. Soc. 133 (2005).
FORMULA
Sum of binomial(prime(n), i)*binomial(prime(n), j)*binomial(prime(n), k) where i+j+k = prime(n) and i,j,k > 0 (see combinatorial identity on page 3471 in Chun-Gang Ji's paper).
MATHEMATICA
Table[Binomial[3 Prime[n], Prime[n]] - 3 Binomial[2 Prime[n], Prime[n]] + 3, {n, 20}]
Binomial[3#, #]-3Binomial[2#, #]+3&/@Prime[Range[20]] (* Harvey P. Dale, Jul 29 2021 *)
PROG
(Magma) [Binomial(3*p, p)-3*Binomial(2*p, p)+3: p in PrimesUpTo(50)];
(PARI) lista(nn) = {forprime(p=2, nn, print1(binomial(3*p, p) - 3*binomial(2*p, p) + 3, ", ")); } \\ Altug Alkan, May 05 2016
CROSSREFS
Sequence in context: A017307 A167725 A366181 * A060629 A373448 A287228
KEYWORD
nonn
AUTHOR
Vincenzo Librandi, May 05 2016
STATUS
approved