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A136507
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a(n) = Sum_{k=0..n} C(2^(n-k) + k, n-k).
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4
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1, 3, 10, 71, 1925, 203904, 75214965, 94608676477, 409763735870986, 6208539881584781823, 334272186911271376874561, 64832512634295914941490910360, 45811927207957062190019240099653265
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| G.f.: A(x) = Sum_{n>=0} (1 - x - 2^n*x^2)^(-1) * log(1 + 2^n*x)^n/n! .
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PROG
| (PARI) {a(n)=sum(k=0, n, binomial(2^(n-k)+k, n-k))} (PARI) /* a(n) = coefficient of x^n in o.g.f. series: */ {a(n)=polcoeff(sum(i=0, n, 1/(1-x-2^i*x^2 +x*O(x^n))*log(1+2^i*x +x*O(x^n))^i/i!), n)}
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CROSSREFS
| Cf. A014070 (C(2^n, n)), A136505 (C(2^n+1, n)), A136506 (C(2^n+2, n)); A136508, A136509.
Sequence in context: A047833 A047834 A181075 * A086846 A082245 A158033
Adjacent sequences: A136504 A136505 A136506 * A136508 A136509 A136510
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Jan 01 2008
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