A375682 -id:A375682 - cp's OEIS frontend

A375237 Expansion of e.g.f. 1 / (1 + x * log(1 - x^2/2))^2.

1, 0, 0, 6, 0, 30, 540, 420, 15120, 192780, 623700, 15467760, 187110000, 1394593200, 30353483160, 401350950000, 4974611241600, 105201040744800, 1624218256861200, 27525899782180800, 599214125325816000, 10967831645346576000, 227431647445400798400

Offset: 0

Seiichi Manyama, Aug 23 2024

nonn

Cf. A375167, A375682.

my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x*log(1-x^2/2))^2))

a(n) = n!*sum(k=0, n\2, (n-2*k+1)!*abs(stirling(k, n-2*k, 1))/(2^k*k!));

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A375167.

a(n) = n! * Sum_{k=0..floor(n/2)} (n-2*k+1)! * |Stirling1(k,n-2*k)|/(2^k*k!).

A375686 Expansion of e.g.f. 1 / (1 + x^2/2 * log(1 - x))^3.

Original entry on oeis.org

1, 0, 0, 9, 18, 60, 1350, 9072, 65520, 984960, 11627280, 135883440, 2109317760, 33214821120, 529403146272, 9536973415200, 182108114697600, 3599078480524800, 76130266179974400, 1701744508586747520, 39652022068801632000, 970411293528131750400

Offset: 0

Seiichi Manyama, Aug 24 2024

nonn

Cf. A351505, A375685.

Cf. A375682.

my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x^2/2*log(1-x))^3))

a(n) = n!*sum(k=0, n\3, (k+2)!*abs(stirling(n-2*k, k, 1))/(2^k*(n-2*k)!))/2;

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A351505.

a(n) = (n!/2) * Sum_{k=0..floor(n/3)} (k+2)! * |Stirling1(n-2*k,k)|/(2^k*(n-2*k)!).

cp's OEIS Frontend

A375237 Expansion of e.g.f. 1 / (1 + x * log(1 - x^2/2))^2.

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A375686 Expansion of e.g.f. 1 / (1 + x^2/2 * log(1 - x))^3.

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