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 A246637 Integers of the form (2^(k+1) - 1)/C(k+2,2). 4
 1, 1, 3, 1533, 4870483401, 10632494904416274948861848751148863, 442778652527729430645666843207235634221292901, 8594831104112238244501123836952492157088005557663896974587707618787108, 970692073484990407927190417652798419153 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS The numbers k for which (2^(k+1) - 1)/C(k+2,2) is an integer are given by A246636.  For each such k, (2^(k+1) - 1)/C(k+2,2) is the mean of the numbers in all the rows of Pascal's triangle, from row 0 through row k. LINKS EXAMPLE The sum of the numbers in Pascal's triangle, from row 0 through row 17, is 2^18 - 1 = 262143; the number of such numbers is C(19,2) = 171, and 262143/171 = 1533; thus is in A246637 and 17 is in A246636. MATHEMATICA z = 3000; t = Select[Range[0, z], IntegerQ[(2^(# + 1) - 1)/Binomial[# + 2, 2]] &] (* A246636 *) Table[(2^(t[[n]] + 1) - 1)/Binomial[t[[n]] + 2, 2], {n, 1, 10}]  (*A246637*) CROSSREFS Cf. A246636, A007318. Sequence in context: A285656 A239503 A118050 * A302132 A258720 A262652 Adjacent sequences:  A246634 A246635 A246636 * A246638 A246639 A246640 KEYWORD nonn,easy AUTHOR Clark Kimberling, Sep 01 2014 STATUS approved

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Last modified June 19 12:57 EDT 2021. Contains 345129 sequences. (Running on oeis4.)