A375237 -id:A375237 - cp's OEIS frontend

A375682 Expansion of e.g.f. 1 / (1 + x * log(1 - x^2/2))^3.

1, 0, 0, 9, 0, 45, 1080, 630, 30240, 470610, 1247400, 38170440, 523908000, 3454050600, 87950182320, 1245647403000, 14580569203200, 346019491818000, 5524280291930400, 92520760776444000, 2188180621979352000, 40781057935225608000, 857154570994798876800

Offset: 0

Seiichi Manyama, Aug 23 2024

nonn

Cf. A375167, A375237.

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

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

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A375167.

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

A375685 Expansion of e.g.f. 1 / (1 + x^2/2 * log(1 - x))^2.

Original entry on oeis.org

1, 0, 0, 6, 12, 40, 720, 4788, 34440, 460080, 5246640, 60318720, 879523920, 13298126400, 206628117696, 3575354428800, 65828785276800, 1264510188264960, 25912058505776640, 561351949518931200, 12721171715573529600, 302794615563937781760, 7554095183751745305600

Offset: 0

Seiichi Manyama, Aug 24 2024

nonn

Cf. A351505, A375686.

Cf. A375237.

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

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

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A351505.

a(n) = n! * Sum_{k=0..floor(n/3)} (k+1)! * |Stirling1(n-2*k,k)|/(2^k*(n-2*k)!).

cp's OEIS Frontend

A375682 Expansion of e.g.f. 1 / (1 + x * log(1 - x^2/2))^3.

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A375685 Expansion of e.g.f. 1 / (1 + x^2/2 * log(1 - x))^2.

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