A370085 -id:A370085 - cp's OEIS frontend

A370084 Expansion of e.g.f. exp( Sum_{k>=1} (2k)! (x/2)^k/k ).

1, 1, 7, 199, 15985, 2810401, 916442551, 497173378087, 416055798439009, 508038355486018945, 867346995542879712871, 2001283948891590010467271, 6070787760933663329315253457, 23660956435620796919900079644449

Offset: 0

Seiichi Manyama, Feb 08 2024

nonn

Cf. A158876, A370085.

Cf. A370086.

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

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

A370087 Expansion of e.g.f. exp( Sum_{k>=1} (3k)!/k! (x/6)^k/k ).

Original entry on oeis.org

1, 1, 11, 591, 95001, 34158801, 23091398451, 26242572454911, 46391926016144241, 120482101765570623201, 439905589366043539453851, 2180755271892747703236167151, 14267395360715456605222995351561, 120323721300147111590970495558478641

Offset: 0

Seiichi Manyama, Feb 08 2024

nonn

Cf. A014606, A370085.

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

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

cp's OEIS Frontend

A370084 Expansion of e.g.f. exp( Sum_{k>=1} (2k)! (x/2)^k/k ).

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A370087 Expansion of e.g.f. exp( Sum_{k>=1} (3k)!/k! (x/6)^k/k ).

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cp's OEIS Frontend

A370084 Expansion of e.g.f. exp( Sum_{k>=1} (2*k)! * (x/2)^k/k ).

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Author

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PARI

Formula

A370087 Expansion of e.g.f. exp( Sum_{k>=1} (3*k)!/k! * (x/6)^k/k ).

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Author

Keywords

Crossrefs

Programs

PARI

Formula

A370084 Expansion of e.g.f. exp( Sum_{k>=1} (2k)! (x/2)^k/k ).

A370087 Expansion of e.g.f. exp( Sum_{k>=1} (3k)!/k! (x/6)^k/k ).