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 A007443 Binomial transform of primes. (Formerly M1436) 12
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Seiichi Manyama, Table of n, a(n) for n = 1..3000 (terms 1..1000 from Vincenzo Librandi) N. J. A. Sloane, Transforms FORMULA a(n) = Sum_{k=1..n} binomial(n-1,k-1)*prime(k). - M. F. Hasler, Jun 02 2017 G.f.: Sum_{k>=1} prime(k)*x^k/(1 - x)^k. - Ilya Gutkovskiy, Apr 21 2019 MAPLE 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 PROG (PARI) A007443(n)=sum(k=1, n, binomial(n-1, k-1)*prime(k)) \\ M. F. Hasler, Jun 02 2017 CROSSREFS Cf. A164738. - Gary W. Adamson, Aug 23 2009 Cf. A001043, A096277, A096278, A096279. See A287915 for indices of primes. First differences give A178167. Sequence in context: A292507 A307465 A116703 * A120925 A086588 A077939 Adjacent sequences:  A007440 A007441 A007442 * A007444 A007445 A007446 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Vladimir Joseph Stephan Orlovsky, May 21 2010 STATUS approved

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Last modified June 2 07:15 EDT 2020. Contains 334767 sequences. (Running on oeis4.)