A385304 Expansion of e.g.f. 1/(1 - 2 * sinh(x))^(1/2).
1, 1, 3, 16, 117, 1096, 12543, 169576, 2644617, 46735936, 922993083, 20145579136, 481555537917, 12511452674176, 351058439096823, 10579734482269696, 340820224678288017, 11687491783287586816, 425075150516293691763, 16343274366458168160256, 662325275389743380902917
Offset: 0
Keywords
Crossrefs
Programs
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PARI
a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j)); a001147(n) = prod(k=0, n-1, 2*k+1); a(n) = sum(k=0, n, a001147(k)*a136630(n, k));
Formula
a(n) ~ sqrt(2) * n^n / (5^(1/4) * exp(n) * log((1 + sqrt(5))/2)^(n + 1/2)). - Vaclav Kotesovec, Jun 28 2025