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Search: id:A137634
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| A137634 |
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Square array where T(n,k) = Sum_{j=0..k} C(n+2*j,j)*C(n+2*j,k-j), read by antidiagonals. |
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5
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| 1, 1, 2, 1, 4, 10, 1, 6, 19, 46, 1, 8, 32, 94, 226, 1, 10, 49, 170, 474, 1136, 1, 12, 70, 282, 899, 2431, 5810, 1, 14, 95, 438, 1577, 4764, 12609, 30080, 1, 16, 124, 646, 2600, 8701, 25318, 65972, 157162, 1, 18, 157, 914, 4076, 15000, 47682, 134964, 347524, 826992
(list; table; graph; listen)
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OFFSET
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0,3
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FORMULA
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G.f.: A(x,y) = R(y)/(1 - x*G(y)), so that the g.f. of row n = R(y)*G(y)^n, where R(y) = 1/sqrt(1-4*y*(1+y)^2) and G(y) = (1-sqrt(1-4*y*(1+y)^2))/(2*y*(1+y)) is the g.f. of A073157.
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EXAMPLE
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Square array begins:
1, 2, 10, 46, 226, 1136, 5810, 30080, 157162, ...;
1, 4, 19, 94, 474, 2431, 12609, 65972, 347524, ...;
1, 6, 32, 170, 899, 4764, 25318, 134964, 721562, ...;
1, 8, 49, 282, 1577, 8701, 47682, 260384, 1419436, ...;
1, 10, 70, 438, 2600, 15000, 85102, 477808, 2664539, ...;
1, 12, 95, 646, 4076, 24643, 145099, 839620, 4800849, ...;
1, 14, 124, 914, 6129, 38868, 237842, 1420660, 8342297, ...;
1, 16, 157, 1250, 8899, 59201, 376740, 2325088, 14036647, ...; ...
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PROGRAM
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(PARI) {T(n, k)=sum(j=0, k, binomial(n+2*j, j)*binomial(n+2*j, k-j))} /* Using the g.f.: */ {T(n, k)=local(Oy=y*O(y^(n+k))); polcoeff(polcoeff(1/sqrt(1-4*y*(1+y)^2+Oy)* 1/(1-x*((1-sqrt(1-4*y*(1+y)^2+Oy))/(2*y*(1 + y+Oy))+x*O(x^n))), n, x), k, y)}
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CROSSREFS
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Cf. A137635, A137636, A137637, A137638, A073157.
Sequence in context: A006445 A097949 A117338 this_sequence A100229 A071949 A156919
Adjacent sequences: A137631 A137632 A137633 this_sequence A137635 A137636 A137637
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KEYWORD
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nonn,tabl
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jan 31 2008
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