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A007443
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Binomial transform of primes.
(Formerly M1436)
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13
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2, 5, 13, 33, 83, 205, 495, 1169, 2707, 6169, 13889, 30993, 68701, 151469, 332349, 725837, 1577751, 3413221, 7349029, 15751187, 33616925, 71475193, 151466705, 320072415, 674721797, 1419327223, 2979993519, 6245693407, 13068049163
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OFFSET
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1,1
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COMMENTS
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Equals row sums of triangle A164738. Example: a(4) = 33 = sum of terms in row 4 of triangle A164738: (2, 3, 5, 3, 5, 7, 5, 3). - Gary W. Adamson, Aug 23 2009
It might have been more natural to define this sequence with offset 0, which would also make the formula simpler. Then a(n) would be the first term of the sequence obtained from the primes by applying n times the operation "take sums of successive terms", Ts(k) = s(k)+s(k+1). - M. F. Hasler, Jun 02 2017
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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a(n) = Sum_{k=1..n} binomial(n-1,k-1)*prime(k). - M. F. Hasler, Jun 02 2017
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MAPLE
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a:=n->add(binomial(n-1, k-1)*ithprime(k), k=1..n): seq(a(n), n=1..30); # Muniru A Asiru, Oct 23 2018
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MATHEMATICA
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A007443[n_]:=Sum[Binomial[n-1, k-1]Prime[k], {k, n}]; Array[A007443, 50] (* or *)
Module[{nmax=50, b}, b=Prime[Range[nmax]]; Join[{2}, Table[First[b=ListConvolve[{1, 1}, b]], nmax-1]]] (* Paolo Xausa, Oct 31 2023 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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