A381757 Expansion of exp( Sum_{k>=1} binomial(7*k-1,2*k-1) * x^k/k ).

1, 6, 161, 6062, 265868, 12720904, 643915209, 33905228350, 1838102210977, 101910583801012, 5751779249830131, 329359930638541776, 19087504000780665541, 1117418973753045781944, 65982722733895652916539, 3925378032146863676341770, 235048328495265879957413946

Offset: 0

Author

Seiichi Manyama, Mar 06 2025

Keywords

• nonn
• easy

Crossrefs

Cf. A006013, A079489, A182960, A381751, A381752, A381753, A381758.

Cf. A300386.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(exp(sum(k=1, N, binomial(7*k-1, 2*k-1)*x^k/k)))

Formula

a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} binomial(7*k-1,2*k-1) * a(n-k).

G.f.: B(x)^2, where B(x) is the g.f. of A300386.