A370084 -id:A370084 - cp's OEIS frontend

A370085 Expansion of e.g.f. exp( Sum_{k>=1} (3k)! (x/6)^k/k ).

1, 1, 21, 3421, 2232361, 4047831801, 16492042429501, 131524059703672021, 1862832637043775536721, 43582296764832433769579761, 1592318494850388661944336320101, 86870590496672779178378519636679501, 6822481321458299127004125050236325798521

Offset: 0

Seiichi Manyama, Feb 08 2024

nonn

Cf. A158876, A370084.

Cf. A370087.

my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=1, N, (3*k)!*(x/6)^k/k))))

a(0) = 1; a(n) = (n-1)! * Sum_{k=1..n} (3*k)! * a(n-k) / (6^k * (n-k)!).

A370086 Expansion of e.g.f. exp( Sum_{k>=1} (2k)!/k! (x/2)^k/k ).

Original entry on oeis.org

1, 1, 4, 40, 796, 27196, 1437136, 108931264, 11207616400, 1502077491856, 254091983968576, 52922687300496256, 13303823750214614464, 3970706309867394765760, 1387875547214097148600576, 561507863501525383223535616, 260328000140228961840632033536

Offset: 0

Seiichi Manyama, Feb 08 2024

nonn

Cf. A000680, A370084.

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

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

cp's OEIS Frontend

A370085 Expansion of e.g.f. exp( Sum_{k>=1} (3k)! (x/6)^k/k ).

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A370086 Expansion of e.g.f. exp( Sum_{k>=1} (2k)!/k! (x/2)^k/k ).

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cp's OEIS Frontend

A370085 Expansion of e.g.f. exp( Sum_{k>=1} (3*k)! * (x/6)^k/k ).

Views

Author

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Programs

PARI

Formula

A370086 Expansion of e.g.f. exp( Sum_{k>=1} (2*k)!/k! * (x/2)^k/k ).

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Author

Keywords

Crossrefs

Programs

PARI

Formula

A370085 Expansion of e.g.f. exp( Sum_{k>=1} (3k)! (x/6)^k/k ).

A370086 Expansion of e.g.f. exp( Sum_{k>=1} (2k)!/k! (x/2)^k/k ).