A012019 -id:A012019 - cp's OEIS frontend

A373539 Expansion of e.g.f. exp(x/(1 + x^3)^(1/3)).

1, 1, 1, 1, -7, -39, -119, 841, 10641, 59473, -393679, -9119439, -77841719, 453247081, 17769103353, 210702481081, -1002688100959, -65813075987679, -1022777654395679, 3554736409105633, 413233827275657241, 8091508938651283321, -16214426267734966039

Offset: 0

Seiichi Manyama, Jun 09 2024

sign

Cf. A012019, A373540.

Cf. A373517.

a(n) = n!*sum(k=0, n\3, (-1)^k*binomial(n/3-1, k)/(n-3*k)!);

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

a(n) == 1 mod 8.

A373540 Expansion of e.g.f. exp(x/(1 + x^4)^(1/4)).

Original entry on oeis.org

1, 1, 1, 1, 1, -29, -179, -629, -1679, 52921, 672841, 4352041, 19934641, -656794709, -13394641259, -130483743389, -870226287839, 29354743432561, 855880592510161, 11361346027482961, 101129588155349281, -3446498927212733069, -134465010284782027619

Offset: 0

Seiichi Manyama, Jun 09 2024

sign

Cf. A012019, A373539.

Cf. A373519.

a(n) = n!*sum(k=0, n\4, (-1)^k*binomial(n/4-1, k)/(n-4*k)!);

a(n) = n! * Sum_{k=0..floor(n/4)} (-1)^k * binomial(n/4-1,k)/(n-4*k)!.

a(n) == 1 mod 30.

A373538 Expansion of e.g.f. exp(x/(1 + x^2)).

Original entry on oeis.org

1, 1, 1, -5, -23, 61, 961, -209, -64175, -197063, 6153121, 48453571, -775290119, -12038136395, 116706067297, 3475641927031, -17614393396319, -1188106176788879, 782498662651585, 478042340115562507, 1987706898622853641, -223468834844001403859

Offset: 0

Seiichi Manyama, Jun 09 2024

sign

Cf. A012019.

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

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

a(n) == 1 mod 6.

cp's OEIS Frontend

A373539 Expansion of e.g.f. exp(x/(1 + x^3)^(1/3)).

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A373540 Expansion of e.g.f. exp(x/(1 + x^4)^(1/4)).

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Author

Keywords

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PARI

Formula

A373538 Expansion of e.g.f. exp(x/(1 + x^2)).

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Author

Keywords

Crossrefs

Programs

PARI

Formula