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Search: id:A051163
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| A051163 |
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Sequence is defined by property that (a0,a1,a2,a3,...) = binomial transform of (a0,a0,a1,a1,a2,a2,a3,a3,...). |
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+0
8
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| 1, 2, 5, 12, 30, 76, 194, 496, 1269, 3250, 8337, 21428, 55184, 142376, 367916, 952000, 2466014, 6393372, 16586678, 43054344, 111801908, 290412296, 754543052, 1960808160, 5096293794, 13247503540, 34440553562, 89549255592
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Equals the self-convolution of A027826. Also equals antidiagonal sums of symmetric square array A100936. - Paul D. Hanna (pauldhanna(AT)juno.com), Nov 22 2004
Equals eigensequence of triangle A152198 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 28 2008]
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LINKS
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N. J. A. Sloane, Transforms
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FORMULA
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a(n) = 1 + Sum_{k=1..n} Sum_{j=0..n-k} C(k, j)*C(n-k, j)*a(j). G.f. A(x) satisfies: A(x) = A(x^2/(1-x)^2)/(1-x)^2 and A(x^2) = A(x/(1+x))/(1+x)^2. - Paul D. Hanna (pauldhanna(AT)juno.com), Nov 22 2004
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PROGRAM
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(PARI) {a(n)=1+sum(k=1, n, sum(j=0, n-k, binomial(k, j)*binomial(n-k, j)*a(j)))} (PARI) {a(n)=local(A, m); if(n<0, 0, m=1; A=1+O(x); while(m<=n, m*=2; A=subst(A, x, (x/(1-x))^2)/(1-x)); polcoeff(A^2, n))} (Hanna)
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CROSSREFS
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Cf. A051164, A051165, A051166.
Cf. A027826, A100936, A100937.
A152198 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 28 2008]
Sequence in context: A026580 A092247 A108360 this_sequence A051450 A038508 A002026
Adjacent sequences: A051160 A051161 A051162 this_sequence A051164 A051165 A051166
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KEYWORD
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easy,nonn,eigen
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AUTHOR
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Jonas Wallgren (jonwa(AT)ida.liu.se)
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EXTENSIONS
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More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 26 2002
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