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A163353
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G.f.: A(x,y) = Sum_{n>=0,m>=0} (2^m-1)^n*x^n * log(1+y)^m/m!.
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0
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1, 1, 0, 1, 1, 0, 1, 4, 4, 1, 0, 1, 13, 44, 67, 56, 28, 8, 1, 0, 1, 40, 360, 1546, 4144, 7896, 11408, 12866, 11440, 8008, 4368, 1820, 560, 120, 16, 1, 0, 1, 121, 2680, 27550, 180096, 866432, 3308736, 10453960, 27991600, 64472200, 129002640, 225783740
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,8
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FORMULA
| T(n,k) = Sum_{j=0..n} (-1)^(n-j)*C(n,j)*C(2^j,k), k=0..2^n.
Row sums form A000371 (nondegenerate Boolean functions of n variables).
Main diagonal equals A134174 and is defined by the g.f.:
Sum_{n>=0} log(1 + (2^n-1)*x)^n/n!.
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EXAMPLE
| Triangle begins:
1,1;
0,1,1;
0,1,4,4,1;
0,1,13,44,67,56,28,8,1;
0,1,40,360,1546,4144,7896,11408,12866,11440,8008,4368,1820,560,120,16,1;
0,1,121,2680,27550,180096,866432,3308736,10453960,27991600,64472200,129002640,225783740,347370800,471435000,565722640,601080385,565722720,471435600,347373600,225792840,129024480,64512240,28048800,10518300,3365856,906192,201376,35960,4960,496,32,1; ...
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PROG
| (PARI) T(n, k)=sum(j=0, n, (-1)^(n-j)*binomial(n, j)*binomial(2^j, k))
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CROSSREFS
| Cf. A000371 (row sums), A134174 (main diagonal).
Sequence in context: A185057 A048152 A070430 * A164612 A180401 A057270
Adjacent sequences: A163350 A163351 A163352 * A163354 A163355 A163356
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KEYWORD
| nonn,tabf
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Jul 25 2009
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