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 A090011 T(n,k) = number of partitions of binomial(n,k), 0<=k<=n, triangular array read by rows. 2
 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, 1, 30, 17977, 26543660, 3519222692, 3519222692, 26543660, 17977, 30, 1, 1, 42, 89134 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS a(n) = A000041(A007318(n)); T(n,0) = T(n,n) = 1; T(n,1) = T(n,n-1) = A000041(n), n>0. LINKS Indranil Ghosh, Rows 0..20, flattened Eric Weisstein's World of Mathematics, Partition Eric Weisstein's World of Mathematics, Binomial Coefficient EXAMPLE Triangle 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; 1, 30, 17977, 26543660, 3519222692, 3519222692, 26543660, 17977, 30, 1; 1, 42, 89134, 1844349560, 9275102575355, 269232701252579, 9275102575355, 1844349560, 89134, 42, 1; ... MATHEMATICA Flatten[Table[PartitionsP[Binomial[n, k]], {n, 0, 10}, {k, 0, n}]] (* Indranil Ghosh, Feb 21 2017 *) PROG (PARI) T(n, k)=numbpart(binomial(n, k)) for(n=0, 10, for(k=0, n, print1(T(n, k), ", ")); print()) \\ Paul D. Hanna, Jun 14 2013 CROSSREFS Cf. A226659 (row sums), A128855 (central terms). Sequence in context: A261365 A261507 A304942 * A061554 A296373 A088326 Adjacent sequences:  A090008 A090009 A090010 * A090012 A090013 A090014 KEYWORD nonn,tabl AUTHOR Reinhard Zumkeller, Jan 28 2004 EXTENSIONS Data section corrected by Indranil Ghosh, Feb 21 2017 STATUS approved

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Last modified March 18 16:30 EDT 2019. Contains 321292 sequences. (Running on oeis4.)