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A202993 G.f.: A(x) = exp( Sum_{n>=1} sigma(n^4)*x^n/n ), a power series in x with integer coefficients. 5
1, 1, 16, 56, 296, 1052, 4952, 17292, 70512, 249712, 931226, 3212690, 11399590, 38331770, 130310820, 428389292, 1408697596, 4524980036, 14486512316, 45558807176, 142488702483, 439559056419, 1347096766984, 4082169772704, 12286806024269, 36629267989081 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Compare to g.f. of partition numbers: exp( Sum_{n>=1} sigma(n)*x^n/n ), where sigma(n) = A000203(n) is the sum of the divisors of n.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..1000

FORMULA

a(n) = (1/n)*Sum_{k=1..n} sigma(k^4) * a(n-k) for n>0, with a(0)=1.

EXAMPLE

G.f.: A(x) = 1 + x + 16*x^2 + 56*x^3 + 296*x^4 + 1052*x^5 + 4952*x^6 +...

log(A(x)) = x + 31*x^2/2 + 121*x^3/3 + 511*x^4/4 + 781*x^5/5 + 3751*x^6/6 + 2801*x^7/7 + 8191*x^8/8 +...+ A202994(n)*x^n/n +...

PROG

(PARI) {a(n)=polcoeff(exp(sum(m=1, n, sigma(m^4)*x^m/m)+x*O(x^n)), n)}

(PARI) {a(n)=if(n==0, 1, (1/n)*sum(k=1, n, sigma(k^4)*a(n-k)))}

CROSSREFS

Cf. A000203 (sigma), A000041 (partitions), A202994, A156304.

Sequence in context: A304692 A295986 A169882 * A221068 A187277 A316443

Adjacent sequences:  A202990 A202991 A202992 * A202994 A202995 A202996

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Dec 27 2011

STATUS

approved

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Last modified June 17 13:12 EDT 2021. Contains 345080 sequences. (Running on oeis4.)