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Search: id:A121398
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| A121398 |
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Main diagonal of triangle A121400; also equals the partial sums of column 0 (A121399) of the same triangle. |
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+0
3
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| 1, 2, 5, 11, 28, 70, 184, 486, 1313, 3576, 9851, 27319, 76286, 214120, 603858, 1709719, 4857959, 13845948, 39572583, 113380652, 325576692, 936796592, 2700456452, 7797587816, 22550434989, 65308288346, 189388557677
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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G.f. A(x) = A(x^2*G)*G*(1-x^2*G)/(1-x), where G(x) is the g.f. of the Motzkin numbers (A001006): G = (1 + x*G + x^2*G^2).
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PROGRAM
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(PARI) {a(n)=local(F=1+x+x^2, G=serreverse(x/(F+x^2*O(x^n)))/x, H=1+x, A); for(i=0, n, H=G*subst(H, x, x^2*G)+x^2*O(x^n)); A=(x*H-y*subst(H, x, x*y))/(x*subst(F, x, y)-y); polcoeff(polcoeff(A, n, x), n, y)}
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CROSSREFS
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Cf. A121400 (triangle), A121399 (column 0), A001006 (Motzkin).
Adjacent sequences: A121395 A121396 A121397 this_sequence A121399 A121400 A121401
Sequence in context: A027087 A055227 A124016 this_sequence A000625 A127331 A040998
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jul 27 2006
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