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A108990
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Triangle, read by rows, where the g.f. of row n, R_n(x), is a polynomial of degree n that satisfies: [x^k] R_{n+1}(x) = [x^k] (1 + x*R_n(x))^(n+1) for k=0..n+1, with R_0(x) = 1.
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6
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1, 1, 1, 1, 2, 3, 1, 3, 9, 22, 1, 4, 18, 76, 287, 1, 5, 30, 180, 1025, 5496, 1, 6, 45, 350, 2670, 19656, 139727, 1, 7, 63, 602, 5761, 54096, 495964, 4447234, 1, 8, 84, 952, 10962, 125328, 1411228, 15629720, 170501039, 1, 9, 108, 1416, 19062, 257040
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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EXAMPLE
| The g.f. of row 4 is: 1 + 4*x + 18*x^2 + 76*x^3 + 287*x^4
and equals the initial coefficients from [x^0] to [x^4] in:
(1+ x*R_3(x))^4 = (1 + x*(1 + 3*x + 9*x^2 + 22*x^3))^4.
Triangle begins:
1;
1,1;
1,2,3;
1,3,9,22;
1,4,18,76,287;
1,5,30,180,1025,5496;
1,6,45,350,2670,19656,139727;
1,7,63,602,5761,54096,495964,4447234;
1,8,84,952,10962,125328,1411228,15629720,170501039; ...
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PROG
| (PARI) {T(n, k)=local(F=1+x*O(x^n)); if(n<k|k<0, 0, for(m=1, n, F=(1+x*F)^m); polcoeff(F, k))}
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CROSSREFS
| Cf. A108991, A108992, A108993, A108994, A108995, A108996.
Sequence in context: A111589 A010027 A151880 * A145080 A065078 A203989
Adjacent sequences: A108987 A108988 A108989 * A108991 A108992 A108993
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KEYWORD
| nonn,tabl
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Jun 15 2005
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