A373577 Expansion of e.g.f. exp(x * (1 + x^2)^(3/2)).
1, 1, 1, 10, 37, 136, 1261, 6616, 45865, 479872, 3206521, 31165696, 356045581, 3082798720, 37528974757, 443190912256, 4792765859281, 69943918698496, 875123733523825, 11059833224507392, 179428023035501941, 2557848382674927616, 37699048392962570461
Offset: 0
Keywords
Programs
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PARI
a(n) = n!*sum(k=0, n\2, binomial(3*n/2-3*k, k)/(n-2*k)!);
Formula
a(n) = n! * Sum_{k=0..floor(n/2)} binomial(3*n/2-3*k,k)/(n-2*k)!.
a(n) == 1 mod 9.