0,3

Compare the first and 2nd binomial transforms of this sequence first binomial={1,1,-2,1,4,1,-62,1,1384,1,-50522,1,2702764,..}; 2nd binomial={1,2,1,-1,1,17,1,-271,1,7937,1,-353791,..}; to that of the first and 2nd binomial transforms of A090145: first binomial of A090145={1,0,1,-3,1,15,1,-273,1,7935,1,..}; 2nd binomial of A090145={1,1,2,1,-4,1,62,1,-1384,1,50522,..}. Comparison reveals this e.g.f. relation of the two sequences: e.g.f.: exp(x)G090158(x)+exp(2x)G090145(x)=2+2sinh(x); e.g.f.: exp(2x)G090158(x)-exp(x)G090145(x)=2sinh(x); thus G090158(x)=2*(1+sinh(x)+exp(x)*sinh(x))/(exp(x)*(1+exp(2*x))) G090145(x)=2*((1+sinh(x))*exp(x)-sinh(x))/(exp(x)*(1+exp(2*x))).

E.g.f.: 2*(1+sinh(x)+exp(x)*sinh(x))/(exp(x)*(1+exp(2*x))). a(2n) = 1 - 2^(2n); 1 = sum_{k=0..2n-1} C(2n-1, k)*a(k); 1 = sum_{k=0..2n} 2^(2n-k)*C(2n, k)*a(k).

Cf. A090145.

Sequence in context: A056287 A050005 A077932 this_sequence A030342 A061966 A085328

Adjacent sequences: A090155 A090156 A090157 this_sequence A090159 A090160 A090161

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Paul D. Hanna (pauldhanna(AT)juno.com), Nov 22 2003