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 A307800 Binomial transform of least common multiple sequence (A003418), starting with a(1). 0
 1, 3, 11, 37, 153, 551, 2023, 7701, 29417, 107083, 384771, 1408133, 5457961, 22466367, 92977823, 365613181, 1342359393, 4677908531, 16159185307, 58676063493, 231520762361, 967464685783, 4052593703511, 16354948948517, 62709285045913, 229276436653851 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Jackson Earles, Aaron Li, Adam Nelson, Marlo Terr, Sarah Arpin, and Ilia Mishev Binomial Transforms of Sequences, CU Boulder Experimental Math Lab, Spring 2019. FORMULA a(n) = Sum_{k=0..n} binomial(n,k)*A003418(k+1). Formula for values modulo 10: (Proof by considering the formula modulo 10)     a(n) (mod 10) = 1, if n = 0, 2 (mod 5),     a(n) (mod 10) = 3, if n = 1, 4 (mod 5),     a(n) (mod 10) = 7, if n = 3 (mod 5). EXAMPLE For n = 3, a(3) = binomial(3,0)*1 + binomial(3,1)*2 + binomial(3,2)*6 + binomial(3,3)*12 = 37. MAPLE b:= proc(n) option remember; `if`(n=0, 1, ilcm(n, b(n-1))) end: a:= n-> add(b(i+1)*binomial(n, i), i=0..n): seq(a(n), n=0..30);  # Alois P. Heinz, Apr 29 2019 MATHEMATICA Table[Sum[Binomial[n, k]*Apply[LCM, Range[k+1]], {k, 0, n}], {n, 0, 30}] (* Vaclav Kotesovec, Jun 06 2019 *) PROG (Sage) def OEISbinomial_transform(N, seq):     BT = [seq[0]]     k = 1     while k< N:         next = 0         j = 0         while j <=k:             next = next + ((binomial(k, j))*seq[j])             j = j+1         BT.append(next)         k = k+1     return BT LCMSeq = [] for k in range(1, 26):     LCMSeq.append(lcm(range(1, k+1))) OEISbinomial_transform(25, LCMSeq) (PARI) a(n) = sum(k=0, n, binomial(n, k)*lcm(vector(k+1, i, i))); \\ Michel Marcus, Apr 30 2019 CROSSREFS Binomial transform of A003418 (shifted). Sequence in context: A047102 A109000 A183511 * A265796 A129962 A026361 Adjacent sequences:  A307797 A307798 A307799 * A307801 A307802 A307803 KEYWORD nonn AUTHOR Sarah Arpin, Apr 29 2019 STATUS approved

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Last modified March 28 07:59 EDT 2020. Contains 333079 sequences. (Running on oeis4.)