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A107593
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Self-convolution of A107592.
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1
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1, 2, 7, 32, 169, 976, 5989, 38398, 254509, 1731596, 12032874, 85092944, 610714311, 4439136084, 32626373027, 242153129074, 1813069499846, 13682961621602, 104014376985334, 796004610604094, 6129901459731357, 47484532009772272
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| G.f. satisfies: A(x) = Sum_{n>=0} x^n * A(x)^((n+1)*(n+2)/4). G.f. A(x) = (1/x)*series-reversion(x/G107590(x)^2) and thus A(x) = G107590(x*A(x))^2 where G107590(x) is the g.f. of A107590.
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EXAMPLE
| A = A^(1/2) + x*A^(3/2) + x^2*A^(6/2) + x^3*A^(10/2) +...
= 1 + 2*x + 7*x^2 + 32*x^3 + 169*x^4 + 976*x^5 + 5989*x^6 +...
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PROG
| (PARI) {a(n)=local(A=1+x+x*O(x^n)); for(k=1, n, A=1+sum(j=1, n, x^j*A^((j+1)*(j+2)/2-1)+x*O(x^n))); polcoeff(A^2, n)}
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CROSSREFS
| Cf. A107590, A107591, A107592.
Sequence in context: A108524 A006781 A115197 * A125277 A179488 A191809
Adjacent sequences: A107590 A107591 A107592 * A107594 A107595 A107596
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), May 17 2005
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