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 A226659 Sum_{k=0..n} A000041( binomial(n,k) ), where A000041(n) is the number of partitions of n. 2
 1, 2, 4, 8, 23, 100, 1003, 31382, 5149096, 7091568720, 287786595280763, 539018517346414192796, 1130813038175196801809538188145, 2336855300714703790840987155549462486654700, 7636154577344556445476348286247799105605643795614728449082014 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Compare to the number of partitions of 2^n (A068413). LINKS Indranil Ghosh, Table of n, a(n) for n = 0..20 FORMULA Row sums of triangle A090011. EXAMPLE Equals the row sums of triangle A090011, which begins: 1; 1, 1; 1, 2, 1; 1, 3, 3, 1; 1, 5, 11, 5, 1; 1, 7, 42, 42, 7, 1; 1, 11, 176, 627, 176, 11, 1; 1, 15, 792, 14883, 14883, 792, 15, 1; 1, 22, 3718, 526823, 4087968, 526823, 3718, 22, 1; ... MATHEMATICA Table[Sum[PartitionsP[Binomial[n, k]], {k, 0, n}], {n, 0, 20}] (* Indranil Ghosh, Feb 21 2017 *) PROG (PARI) {a(n)=sum(k=0, n, numbpart(binomial(n, k)))} for(n=0, 15, print1(a(n), ", ")) CROSSREFS Cf. A090011, A068413, A128855, A000041. Sequence in context: A295419 A290816 A181070 * A009327 A027168 A078751 Adjacent sequences: A226656 A226657 A226658 * A226660 A226661 A226662 KEYWORD nonn AUTHOR Paul D. Hanna, Jun 14 2013 STATUS approved

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Last modified August 13 17:42 EDT 2024. Contains 375144 sequences. (Running on oeis4.)