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 A362125 Square array T(n,k), n>=0, k>=0, read by antidiagonals downwards, where column k is the expansion of 1/(1 - x*(1+x)^k)^k. 1
 1, 1, 0, 1, 1, 0, 1, 2, 2, 0, 1, 3, 7, 3, 0, 1, 4, 15, 18, 5, 0, 1, 5, 26, 55, 47, 8, 0, 1, 6, 40, 124, 198, 118, 13, 0, 1, 7, 57, 235, 571, 681, 290, 21, 0, 1, 8, 77, 398, 1320, 2500, 2263, 702, 34, 0, 1, 9, 100, 623, 2640, 7026, 10504, 7341, 1677, 55, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 LINKS Table of n, a(n) for n=0..65. FORMULA T(n,k) = Sum_{j=0..n} (-1)^j * binomial(-k,j) * binomial(k*j,n-j) = Sum_{j=0..n} binomial(j+k-1,j) * binomial(k*j,n-j). EXAMPLE Square array begins: 1, 1, 1, 1, 1, 1, ... 0, 1, 2, 3, 4, 5, ... 0, 2, 7, 15, 26, 40, ... 0, 3, 18, 55, 124, 235, ... 0, 5, 47, 198, 571, 1320, ... 0, 8, 118, 681, 2500, 7026, ... PROG (PARI) T(n, k) = sum(j=0, n, binomial(j+k-1, j)*binomial(k*j, n-j)); CROSSREFS Columns k=0..2 give A000007, A000045(n+1), A362126. Main diagonal gives A362080. Cf. A362078, A362079. Sequence in context: A294498 A292860 A265609 * A261718 A144074 A261780 Adjacent sequences: A362122 A362123 A362124 * A362126 A362127 A362128 KEYWORD nonn,tabl AUTHOR Seiichi Manyama, Apr 08 2023 STATUS approved

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Last modified May 26 01:34 EDT 2024. Contains 372807 sequences. (Running on oeis4.)