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A234855 E.g.f. satisfies: A(x) = Sum_{n>=0} ( Integral A(x)^n dx )^n. 2
1, 1, 3, 21, 241, 3951, 85499, 2325205, 76860673, 3014656183, 137784836475, 7235668490589, 431692029451009, 28991550501283359, 2174713803535479419, 181001542259074421413, 16618721538838243841185, 1674634828088234390862727, 184352162064651888588105243 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Paul D. Hanna, Table of n, a(n) for n = 0..100

FORMULA

E.g.f. satisfies: A'(x) = Sum_{n>=1} n * A(x)^n * ( Integral A(x)^n dx )^(n-1).

EXAMPLE

E.g.f.: A(x) = 1 + x + 3*x^2/2! + 21*x^3/3! + 241*x^4/4! + 3951*x^5/5! +...

To illustrate how the terms are generated, form a table of coefficients of x^k/k!, k>=0, in (Integral A(x)^n dx)^n for n>=0 like so:

n=0: [1, 0, 0,  0,   0,    0,     0,      0,        0,         0, ...];

n=1: [0, 1, 1,  3,  21,  241,  3951,  85499,  2325205,  76860673, ...];

n=2: [0, 0, 2, 12,  88,  920, 13328, 254744,  6161568, 182632584, ...];

n=3: [0, 0, 0,  6, 108, 1710, 29700, 600642, 14344092, 403670790, ...];

n=4: [0, 0, 0,  0,  24,  960, 28800, 826560, 24665088, 793449216, ...];

n=5: [0, 0, 0,  0,   0,  120,  9000, 462000, 20958000, 922005000, ...];

n=6: [0, 0, 0,  0,   0,    0,   720,  90720,  7378560, 504040320, ...];

n=7: [0, 0, 0,  0,   0,    0,     0,   5040,   987840, 120022560, ...];

n=8: [0, 0, 0,  0,   0,    0,     0,      0,    40320,  11612160, ...];

n=9: [0, 0, 0,  0,   0,    0,     0,      0,        0,    362880, ...]; ...

then the column sums form the terms of this sequence.

PROG

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=sum(k=0, 30, intformal( (A+x*O(x^n))^k )^k)); n!*polcoeff(A, n)}

for(n=0, 20, print1(a(n), ", "))

CROSSREFS

Cf. A232552, A107595.

Sequence in context: A138903 A302703 A334262 * A058562 A145083 A234303

Adjacent sequences:  A234852 A234853 A234854 * A234856 A234857 A234858

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jan 01 2014

STATUS

approved

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Last modified January 20 09:55 EST 2022. Contains 350471 sequences. (Running on oeis4.)