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A103370
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Row sums of triangle A095801 (matrix square of the Narayana triangle A001263).
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2
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1, 3, 12, 57, 303, 1743, 10629, 67791, 448023, 3047745, 21235140, 150969195, 1091936745, 8016114681, 59616180828, 448459155063, 3407842605039, 26131449100821, 202011445055436, 1573171285950639, 12333030718989969
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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FORMULA
| G.f. satisfies: A(x) = B(x)^3 where A(x) = Sum_{n>=0} a(n)*x^n/[n!*(n+1)!/2^n] and B(x) = Sum_{n>=0} x^n/[n!*(n+1)!/2^n]. [From Paul D. Hanna (pauldhanna(AT)juno.com), Feb 01 2009]
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EXAMPLE
| Contribution from Paul D. Hanna (pauldhanna(AT)juno.com), Feb 01 2009: (Start)
G.f.: A(x) = 1 + 3*x + 12*x^2/3 + 57*x^3/18 + 303*x^4/180 + 1743*x^5/2700 +...+ x^n/[n!*(n+1)!/2^n] +...
A(x) = B(x)^3 where:
B(x) = 1 + x + x^2/3 + x^3/18 + x^4/180 + x^5/2700 +...+ x^n/[n!*(n+1)!/2^n] +... (End)
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PROG
| (PARI) {a(n)=if(n<1, 0, sum(k=1, n, (matrix(n, n, m, j, binomial(m-1, j-1)*binomial(m, j-1)/j)^2)[n, k]))}
(PARI) {a(n)=local(B=sum(k=0, n, x^k/(k!*(k+1)!/2^k))+x*O(x^n)); polcoeff(B^3, n)*n!*(n+1)!/2^n} [From Paul D. Hanna (pauldhanna(AT)juno.com), Feb 01 2009]
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CROSSREFS
| Cf. A095801, A001263.
Cf. A008277, A000108.
Sequence in context: A047891 A166991 A151498 * A094149 A117107 A159609
Adjacent sequences: A103367 A103368 A103369 * A103371 A103372 A103373
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Feb 02 2005
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