A354250 -id:A354250 - cp's OEIS frontend

A354243 Expansion of e.g.f. Sum_{k>=0} (2k)! log(1+x)^k / k!.

1, 2, 22, 652, 36252, 3249648, 427841136, 77725790784, 18629187576192, 5694658698037824, 2162203542669622464, 998275836346954738560, 550745779092109449586560, 357819370067278253918223360, 270404811566689476740771496960

Offset: 0

Seiichi Manyama, May 20 2022

nonn

Cf. A006252, A354250.

Cf. A316747, A354240, A354244.

my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (2*k)!*log(1+x)^k/k!)))

a(n) = sum(k=0, n, (2*k)!*stirling(n, k, 1));

a(n) = Sum_{k=0..n} (2*k)! * Stirling1(n,k).

A354251 Expansion of e.g.f. Sum_{k>=0} (3k)! (-log(1-x))^k / k!.

Original entry on oeis.org

1, 6, 726, 365052, 481186836, 1312477120944, 6422029618230000, 51225621215200895520, 621881012244669445985760, 10911233517605729917096273920, 265743399210784245852461349120000, 8697920910678436598411074217669652480

Offset: 0

Seiichi Manyama, May 21 2022

nonn

Cf. A007840, A354244.

Cf. A316748, A353118, A354250.

my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (3*k)!*(-log(1-x))^k/k!)))

a(n) = sum(k=0, n, (3*k)!*abs(stirling(n, k, 1)));

a(n) = Sum_{k=0..n} (3*k)! * |Stirling1(n,k)|.

cp's OEIS Frontend

A354243 Expansion of e.g.f. Sum_{k>=0} (2k)! log(1+x)^k / k!.

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A354251 Expansion of e.g.f. Sum_{k>=0} (3k)! (-log(1-x))^k / k!.

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cp's OEIS Frontend

A354243 Expansion of e.g.f. Sum_{k>=0} (2*k)! * log(1+x)^k / k!.

Views

Author

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Programs

PARI

PARI

Formula

A354251 Expansion of e.g.f. Sum_{k>=0} (3*k)! * (-log(1-x))^k / k!.

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Author

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PARI

PARI

Formula

A354243 Expansion of e.g.f. Sum_{k>=0} (2k)! log(1+x)^k / k!.

A354251 Expansion of e.g.f. Sum_{k>=0} (3k)! (-log(1-x))^k / k!.