A381751 Expansion of exp( Sum_{k>=1} binomial(8*k-1,2*k-1) * x^k/k ).

1, 7, 252, 12866, 767460, 50005591, 3449225652, 247579862356, 18301102679444, 1383742325041292, 106516121515030768, 8319491960857739258, 657680525420544788060, 52522142073165048614002, 4230907373618147894630904, 343379827862952363210331624, 28051180121294369965012932980

Offset: 0

Author

Seiichi Manyama, Mar 06 2025

Keywords

• nonn
• easy

Crossrefs

Cf. A006013, A079489, A182960, A381752, A381753, A381757, A381758.

Cf. A381745.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(exp(sum(k=1, N, binomial(8*k-1, 2*k-1)*x^k/k)))

Formula

a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} binomial(8*k-1,2*k-1) * a(n-k).