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 A274741 Table of coefficients in functions that satisfy W_n(x) = W_{n-1}(x)^W_n(x), with W_0(x) = exp(x), as read by antidiagonals. 1
 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 16, 5, 1, 1, 1, 125, 43, 7, 1, 1, 1, 1296, 525, 82, 9, 1, 1, 1, 16807, 8321, 1345, 133, 11, 1, 1, 1, 262144, 162463, 28396, 2729, 196, 13, 1, 1, 1, 4782969, 3774513, 734149, 71721, 4821, 271, 15, 1, 1, 1, 100000000, 101808185, 22485898, 2300485, 151376, 7765, 358, 17, 1, 1, 1, 2357947691, 3129525793, 796769201, 87194689, 5787931, 283321, 11705, 457, 19, 1, 1, 1, 61917364224, 108063152091, 32084546824, 3815719969, 261066156, 12567187, 486396, 16785, 568, 21, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS See examples and formulas at A274391, which is the main entry for this table. This entry is the same as table A274391, but read by antidiagonals from top down. LINKS FORMULA See formulas at A274391, which is the main entry for this table. EXAMPLE See examples at A274391, which is the main entry for this table. This table begins: 1, 1,  1,   1,     1,       1,         1,          1, ...; 1, 1,  3,  16,   125,    1296,     16807,     262144, ...; 1, 1,  5,  43,   525,    8321,    162463,    3774513, ...; 1, 1,  7,  82,  1345,   28396,    734149,   22485898, ...; 1, 1,  9, 133,  2729,   71721,   2300485,   87194689, ...; 1, 1, 11, 196,  4821,  151376,   5787931,  261066156, ...; 1, 1, 13, 271,  7765,  283321,  12567187,  656778529, ...; 1, 1, 15, 358, 11705,  486396,  24539593, 1457297878, ...; ... This table may also be written as a triangle: 1; 1, 1; 1, 1, 1; 1, 3, 1, 1; 1, 16, 5, 1, 1; 1, 125, 43, 7, 1, 1; 1, 1296, 525, 82, 9, 1, 1; 1, 16807, 8321, 1345, 133, 11, 1, 1; 1, 262144, 162463, 28396, 2729, 196, 13, 1, 1; 1, 4782969, 3774513, 734149, 71721, 4821, 271, 15, 1, 1; 1, 100000000, 101808185, 22485898, 2300485, 151376, 7765, 358, 17, 1, 1; ... PROG (PARI) {ITERATE(F, n, k) = my(G=x +x*O(x^k)); for(i=1, n, G=subst(G, x, F)); G} {T(n, k) = my(TREE = serreverse(x*exp(-x +x*O(x^k)))); k!*polcoeff(exp(ITERATE(TREE, n, k)), k)} /* Print this table as a rectangular array */ for(n=0, 10, for(k=0, 10, print1(T(n, k), ", ")); print("")) /* Print this table as a triangle */ for(n=0, 12, for(k=0, n, print1(T(k, n-k), ", ")); print("") ) /* Print this table as a flattened array */ for(n=0, 12, for(k=0, n, print1(T(k, n-k), ", ")); ) CROSSREFS Cf. A274391. Sequence in context: A265025 A284578 A070989 * A347811 A320412 A286591 Adjacent sequences:  A274738 A274739 A274740 * A274742 A274743 A274744 KEYWORD nonn,tabl AUTHOR Paul D. Hanna, Jul 04 2016 STATUS approved

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Last modified December 8 17:01 EST 2021. Contains 349596 sequences. (Running on oeis4.)