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A346055 Expansion of e.g.f. Product_{k>=1} B(x^k/k) where B(x) = exp(exp(x) - 1) = e.g.f. of Bell numbers. 3
1, 1, 3, 10, 47, 246, 1617, 11586, 97463, 891610, 9189623, 102024396, 1250714445, 16351489116, 232261545869, 3499469551402, 56582677946675, 964734301550142, 17509882651329087, 333381717125596692, 6710286637806825557, 141167551783524139468 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..449

FORMULA

E.g.f.: exp( Sum_{k>=1} (exp(x^k/k) - 1) ).

E.g.f.: exp( Sum_{k>=1} A005225(k)*x^k/k! ).

a(n) = (n-1)! * Sum_{k=1..n} k * (Sum_{d|k} 1/(d! * (k/d)^d)) * a(n-k)/(n-k)! for n > 0.

PROG

(PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(prod(k=1, N, exp(exp(x^k/k)-1))))

(PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=1, N, exp(x^k/k)-1))))

(PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=1, N, sumdiv(k, d, 1/(d!*(k/d)^d))*x^k))))

(PARI) a(n) = if(n==0, 1, (n-1)!*sum(k=1, n, k*sumdiv(k, d, 1/(d!*(k/d)^d))*a(n-k)/(n-k)!));

CROSSREFS

Cf. A000110, A005225, A081066, A209903, A346056, A346057.

Sequence in context: A226879 A226880 A005651 * A249479 A236410 A339836

Adjacent sequences:  A346052 A346053 A346054 * A346056 A346057 A346058

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Jul 02 2021

STATUS

approved

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Last modified May 25 21:17 EDT 2022. Contains 354071 sequences. (Running on oeis4.)