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 A155826 A triangular sequence: t(n,m)=(Binomial[n, m] + Binomial[m*(n - m), n] + 2*((-1)^(n - 2*m)*StirlingS1[n, m]StirlingS1[n, n - m])). 0
 1, 1, 1, 4, 1, 1, 15, 15, 1, 1, 76, 249, 76, 1, 1, 485, 3516, 3516, 485, 1, 1, 3606, 46623, 101354, 46623, 3606, 1, 1, 30247, 617541, 2388107, 2388107, 617541, 30247, 1, 1, 282248, 8416315, 51483931, 91651662, 51483931, 8416315, 282248, 1, 1, 2903049 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Row sums are: {4, 2, 6, 32, 403, 8004, 201814, 6071792, 212016652, 8430651132, 376203306434,...} LINKS FORMULA t(n,m)=(Binomial[n, m] + Binomial[m*(n - m), n] + 2*((-1)^(n - 2*m)*StirlingS1[n, m]StirlingS1[n, n - m])). EXAMPLE {4}, {1, 1}, {1, 4, 1}, {1, 15, 15, 1}, {1, 76, 249, 76, 1}, {1, 485, 3516, 3516, 485, 1}, {1, 3606, 46623, 101354, 46623, 3606, 1}, {1, 30247, 617541, 2388107, 2388107, 617541, 30247, 1}, {1, 282248, 8416315, 51483931, 91651662, 51483931, 8416315, 282248, 1}, {1, 2903049, 119667766, 1071669632, 3021085118, 3021085118, 1071669632, 119667766, 2903049, 1}, {1, 32659210, 1786250293, 22164382836, 91580770746, 145075180262, 91580770746, 22164382836, 1786250293, 32659210, 1} MATHEMATICA t[n_, m_] = (Binomial[n, m] + Binomial[m*(n - m), n] + 2*((-1)^(n - 2*m)*StirlingS1[n, m]StirlingS1[n, n - m])); Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%] CROSSREFS Sequence in context: A176428 A116469 A156599 * A010320 A152571 A008304 Adjacent sequences:  A155823 A155824 A155825 * A155827 A155828 A155829 KEYWORD nonn,tabl,uned AUTHOR Roger L. Bagula, Jan 28 2009 STATUS approved

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Last modified November 29 08:33 EST 2020. Contains 338762 sequences. (Running on oeis4.)